This verse is referring to a man who has potential widowhood and divorce with her, excluding a gentile and a slave, who do not have widowhood and divorce with her, as they cannot marry Jews at all. Therefore, they disqualify a woman from marrying into the priesthood through sexual intercourse, even if she does not have a child with them.

The Gemara asks: We have found a source for the halakha that a gentile and a slave disqualify a priestess. From where do we derive this with regard to a Levite and an Israelite woman? The Gemara answers: It is as Rabbi Abba said that Rav said: The verse “But if a priest’s daughter be a widow, or divorced” (Leviticus 22:13) could have begun with the words: If a priest’s daughter. The word “but,” the prefix vav, expands the prohibition to include additional women. Here too, it may be derived from the distinction between the phrase: If a priest’s daughter, and the phrase as it actually appears in the verse: “But if a priest’s daughter,” that Levite and Israelite women are subject to the prohibition as well.

The Gemara asks: In accordance with whose opinion is this exposition possible? It is in accordance only with the opinion of Rabbi Akiva, as he derives halakhot from the prefix vav. The Gemara responds: Even if you say it is accordance with the Rabbis, the entire phrase: “But if a priest’s daughter,” is superfluous in the verse, as the previous verses had already mentioned the priest’s daughter. Therefore, the inclusion of Levite and Israelite women in the prohibition may be derived from the entire expression.

The Gemara suggests: But perhaps you should say a different interpretation of the mention of widowhood and divorce in the verse: In the case of one who has potential widowhood and divorce with her, if he does not have offspring from her she may partake of teruma upon her widowhood or divorce, whereas if he does have offspring from her she does not partake. However, in the case of one who does not have widowhood and divorce with her, even if she has offspring from him, she should be allowed to partake of teruma, as the offspring is not considered his.

The Gemara answers: If so, why do I need to include a Levite and an Israelite woman? If the daughter of a priest is not disqualified from teruma due to intercourse with a gentile or slave, certainly a Levite or Israelite woman is not. The fact that the verse indicates inclusion of Levite and Israelite women proves that the halakha that is derived from it is a stringency and not a leniency.

The Gemara asks: And according to Rabbi Akiva, who said that betrothal of those who may not engage in intercourse, as they are liable for violating a prohibition, does not take effect, and therefore the meaning of the phrase “And if a priest’s daughter be [tihye] to a common man” (Leviticus 22:12) is not: If she marries him, but rather: If she engages in intercourse with him, why do I need the Torah to mention the phrase “a widow, or divorced” in the verse: “But if a priest’s daughter be a widow, or divorced…she may eat of her father’s bread” (Leviticus 22:13)? It is not necessary for this phrase to teach that a gentile and a slave disqualify a woman from marrying into the priesthood through sexual intercourse, as suggested by Rabbi Yishmael, as they are included in the prohibition proscribing a woman who engaged in intercourse with a man who is unfit for her.

The Gemara answers: A widow is mentioned to be stringent with her, and a divorcée to be lenient with her, and both are necessary. As, had the Torah taught us only the case of a widow, you might have assumed that specifically if this daughter of a priest is a widow she partakes of teruma when she does not have offspring because she is fit for the priesthood, as she may marry a common priest, but with regard to a divorcée, who is not fit for the priesthood at all, you might say that even if she does not have offspring she does not partake of teruma. And had it taught us only the case of a divorcée, you might have assumed that only a divorcée does not partake of teruma when she has offspring from a non-priest because she is not fit for the priesthood, but with regard to a widow, who is fit for the priesthood, you might say that even if she has offspring she should also partake of teruma. It is therefore necessary for both cases to be stated.

The Gemara asks: And perhaps you should say that the category of a woman who engaged in intercourse with a man who is unfit for her and is therefore disqualified from the priesthood applies even to the case of a man remarrying his divorcée after she had been married to another man in the meantime, which is prohibited. The Gemara answers: The Merciful One states in the Torah: “To a common man [ish zar],” literally, a man who is a stranger, “she shall not eat of that which is set apart from the sacred.” The Gemara understands the notion of a stranger to be one whom she was forbidden to marry and interprets homiletically: Only marriage to one who was a stranger, i.e., forbidden, to her from the outset precludes her from partaking of teruma, to the exclusion of one who was not a stranger to her from the outset, such as her ex-husband.

The Gemara asks: If so, a ḥalal, who was not excluded at the outset, as he may marry even the daughter of a priest, should not disqualify a woman from marrying into the priesthood. The Gemara answers that the verse states, with regard to a priest who marries a woman unfit for the priesthood: “He shall not profane his seed among his people” (Leviticus 21:15), thereby juxtaposing his seed to him. Just as he, a priest who married a woman forbidden to him, disqualifies her from the priesthood, so too, his seed, the ḥalal, also disqualifies a woman with whom he engaged in intercourse.

The Gemara asks: And perhaps you should say that a woman who engaged in intercourse with a man unfit for her is disqualified from the time of their betrothal, even before they engaged in intercourse. The Gemara answers that this is similar to a High Priest who engaged in intercourse with a widow: Just as a High Priest who engaged in intercourse with a widow has disqualified her through intercourse, not betrothal, so too, this unfit man has also disqualified her through intercourse.

The Gemara asks: And perhaps you should say that he does not disqualify her until there is both betrothal and intercourse. The Gemara again answers that this is similar to a High Priest who engaged in intercourse with a widow: Just as a High Priest who engaged in intercourse with a widow disqualifies her through intercourse alone, so too, this man also disqualified her through intercourse alone.

§ It was taught in the baraita under discussion (68a) that Rabbi Yosei says: Of the men unfit to enter the assembly of Israel, anyone whose offspring are also unfit disqualifies a woman with whom he engaged in intercourse from the priesthood. However, anyone whose offspring are not unfit does not disqualify her. The Gemara asks: What difference is there between the first tanna of the baraita and Rabbi Yosei?

Rabbi Yoḥanan said: The practical difference between them pertains to a second-generation Egyptian and a second-generation Edomite. The children of these men, i.e., the third generation, may marry Jews of unflawed lineage. Therefore, according to Rabbi Yosei, they too do not disqualify a woman from the priesthood through intercourse with them. The first tanna, however, holds that they have the same status as a first-generation Egyptian or Edomite convert, in that they disqualify a woman from the priesthood through intercourse.

And both tanna’im derived their respective opinions only from the case of a High Priest who engaged in intercourse with a widow, although they reached different conclusions. The first tanna reasoned: Just as with regard to a High Priest who engaged in intercourse with a widow, his act of intercourse with her is a transgression, and therefore he disqualifies her from the priesthood, so too, this man, a second-generation Egyptian or Edomite, also disqualifies her.

And Rabbi Yosei also reasoned: This is like a High Priest who engaged in intercourse with a widow. Just as the High Priest’s children are unfit for the priesthood, and he himself disqualifies the widow from marrying into the priesthood, so too, any man whose children are unfit to marry Jews of unflawed lineage disqualifies a woman with whom he engaged in intercourse from marrying into the priesthood. This inference comes to exclude a second-generation Egyptian, whose children are not unfit, as it is written: “The children of the third generation that are born to them may enter into the assembly of the Lord” (Deuteronomy 23:9).

It is taught in the baraita under discussion that Rabban Shimon ben Gamliel says: Anyone whose daughter you may marry, you may marry his widow; anyone whose daughter you may not marry, you may not marry his widow. The Gemara asks: What difference is there between Rabbi Yosei and Rabban Shimon ben Gamliel? They appear to be stating the same principle, that a man disqualifies a woman from the priesthood only if his children are unfit to marry Jews of unflawed lineage as well.

Ulla said: The practical difference between them is in the case of an Ammonite and a Moabite convert. And both of them derived their respective opinions from none other than the case of a High Priest with a widow. Rabbi Yosei reasoned: Just as with regard to a High Priest who engaged in intercourse with a widow, his children are unfit for the priesthood and he himself disqualifies the widow, so too, any man whose children are unfit disqualifies a woman with whom he engaged in intercourse.

Rabban Shimon ben Gamliel reasoned: Just as in the case of a High Priest who engaged in intercourse with a widow, where all of his children from her are unfit for the priesthood and he disqualifies her as well, so too, in the case of a man all of whose children are unfit, he disqualifies a woman with whom he engaged in intercourse. This is to the exclusion of an Ammonite or a Moabite convert, as not all of his children are unfit to marry Jews of unflawed lineage, as the Master said: An Ammonite man is unfit to enter the assembly but not an Ammonite woman; a Moabite man is unfit but not a Moabite woman. Since only the sons of an Ammonite or Moabite convert are unfit, they do not disqualify a woman with whom they engaged in intercourse from marrying into the priesthood.

MISHNA: In the case of one who rapes a woman without marrying her; or one who seduces a woman without marrying her; or an imbecile who engages in intercourse with a woman, even if he did marry her, if they are non-priests they do not disqualify the daughter of a priest from partaking of teruma, and if they are priests they do not enable an Israelite woman to partake of teruma. And if they are not fit to enter the assembly of Israel through marriage, they disqualify the daughter of a priest from partaking of teruma. How so? If it was an Israelite who engaged in extramarital intercourse with the daughter of a priest, she may partake of teruma, as this act of intercourse does not disqualify her.