Learn from the statement of Rabbi Akiva three halakhot. Learn from it that the removal of leavened bread can be performed only by means of burning. Rabbi Akiva bases his opinion on the fact that it is prohibited to kindle a fire on the Festival.
And second, learn from it that the prohibition against kindling a fire on Shabbat was specifically singled out in the Torah to divide the various primary categories of labor and to establish liability for performance of each of them. The dissenting opinion is that kindling is singled out to teach that there is no capital punishment for performing that primary category of labor.
And third, learn from it that we do not say: Since it is permitted to kindle a fire for the purpose of preparing food, it is also permitted to light a fire not for the purpose of preparing food, e.g., to burn leaven.

The Sages taught in a baraita: “Seven days leaven shall not be found in your houses” (Exodus 12:19). To what purpose does the verse state this prohibition? Wasn’t it already stated: “And no leaven shall be seen with you, neither shall there be leavened bread seen with you, in all your borders” (Exodus 13:7)?

The baraita answers: Because it is stated: “And no leaven shall be seen with you,” which teaches that your own leaven you may not see, but you may see leaven that belongs to others, i.e., gentiles, and leaven consecrated to God. In light of this halakha, I might have thought that one may conceal leaven in one’s home or accept deposits of leaven from a gentile. Therefore, the verse states: “Shall not be found,” meaning that one may not retain any type of leaven in one’s house at all.

The tanna continues: Had only this verse been stated, I would have derived nothing other than this halakha with regard to a gentile whom you did not overcome and who does not dwell with you in the courtyard. With regard to a gentile whom you overcame and who dwells with you in the courtyard, from where do we know that he is also included in this prohibition? The verse states: “It shall not be found in your houses” at all, i.e., anywhere in one’s possession.

The baraita further states that from the verse: “It shall not be found in your houses,” I have derived nothing other than the fact that this prohibition applies to leaven that is actually in your houses. From where is it derived that this halakha applies even to leaven in pits, ditches, and caves? The verse states: In all your borders, i.e., anywhere that belongs to you.

And still I can say: If there is leaven in your houses, one violates the prohibition that leaven shall not be seen and the prohibition that it shall not be found, as well as the prohibitions of you shall not conceal and you shall not receive deposits from a gentile. Meanwhile, in your borders, outside your home, your own leaven you may not see, but you may see leaven that belongs to others, i.e., gentiles, and leaven consecrated to God. From where is it derived that it is proper to apply the prohibition that was said about this place to that place, and the prohibition that was said about that place to this place?

The tanna answers that the verse states the term leaven with regard to houses and the term leaven with regard to borders as a verbal analogy. It states leaven with regard to houses: “Seven days leaven shall not be found in your houses,” and it states leaven with regard to borders: “Neither shall there be leaven seen with you.” Just as for the leaven stated with regard to houses one transgresses the prohibition that leaven shall not be seen and the prohibition that it shall not be found, and the prohibitions of one shall not conceal and one shall not receive deposits from a gentile, so too, for the leaven stated with regard to borders, one transgresses the prohibition that leaven shall not be seen and the prohibition that it shall not be found, and the prohibitions of one shall not conceal and one shall not receive deposits from a gentile.

The converse is also true: Just as concerning the leaven stated with regard to borders, your own leaven you may not see, but you may see leaven that belongs to others, i.e., gentiles, and leaven consecrated to God, so too, concerning the leaven stated with regard to houses: Your own leaven you may not see, but you may see leaven that belongs to others and leaven consecrated to God.

The Gemara addresses several difficult aspects of this baraita. The Master said: I would have derived nothing other than this halakha with regard to a gentile whom you did not overcome and who does not dwell with you in the courtyard. With regard to a gentile whom you overcame and who dwells with you in the courtyard, from where is it derived that he is also included in this prohibition? The verse states: “It shall not be found in your houses.”

The Gemara questions the logic of this proof. On the contrary; the prohibition regarding the leaven of a gentile who is subservient to and lives with a Jew is more obvious than the prohibition regarding the leaven of a gentile who is neither. The tanna should have started with the leaven belonging to a gentile who is subservient to a Jew. Abaye said: Reverse the order of the statement: I might have thought that only leaven owned by a gentile whom you overcame and who dwells with you in the courtyard is prohibited; but leaven owned by a gentile whom you did not overcome and who does not dwell with you in the courtyard is permitted.

Rava said: Actually, do not reverse the order, as this statement is not in fact a continuation of the previous one and instead it applies to the first clause of the baraita, which deals with the time when leaven is permitted. The entire statement should read as follows: Your own leaven you may not see, but you may see leaven that belongs to others, i.e., gentiles, and leaven consecrated to God, as one is not commanded to remove leaven that belongs to a gentile. I have derived nothing other than this halakha with regard to a gentile whom you did not overcome and who does not dwell with you in the courtyard, as the leaven belonging to that gentile is in no way tied to the Jew. With regard to a gentile whom you overcame and who dwells with you in the courtyard, from where is it derived that he is also included in this leniency? The verse states: “It shall not be found.”

The Gemara raises a difficulty: This tanna seeks permission for seeing the leaven of a gentile, and yet he cites a verse to establish a prohibition. The Gemara answers that the tanna did not cite proof from the phrase: It shall not be found. Due to the fact that it is stated: “No leaven shall be seen with you in all your borders” (Exodus 13:7) and “No leaven shall be seen with you in all your borders” (Deuteronomy 16:4) twice, one of them is superfluous and may be appended to: It shall not be found, creating the prohibition: It shall not be found with you. Only leaven belonging to a Jew is prohibited.

The Gemara continues its analysis of the baraita. The Master said: I might have thought that one may conceal leaven in one’s home or accept deposits of leaven from the gentiles. Therefore, the verse states: It shall not be found. The Gemara asks: But didn’t you say in the first clause of the baraita: Your own leaven you may not see, but you may see leaven that belongs to others and leaven consecrated to God, indicating that it is permitted to have leaven in one’s house if it belongs to a gentile?

The Gemara answers: This is not difficult; in this case it is prohibited, as he accepted upon himself responsibility to pay for the leaven if it is destroyed. Therefore, it is considered as though the leaven belonged to him. In that case it is permitted, as he did not accept upon himself responsibility, and therefore the leaven remains the full-fledged property of the gentile.

That ruling is like that which Rava said to the residents of Meḥoza: Remove the leavened bread that belongs to the members of the gentile army from your houses. Gentile soldiers would bring flour with them and force the people in the city to prepare bread on their behalf. Rava explained the rationale for his ruling: Since if the flour were stolen or if it were lost, it stands in your possession and you would be required to pay for it, its legal status is as if it were yours, and it is prohibited to keep it during Passover.

The Gemara raises a difficulty: This explanation works out well according to the one who said: The legal status of an object that effects monetary loss is like that of money. If an item is inherently or currently worthless, but if it is lost or stolen one would be obligated to pay to replace it, its legal status is like that of money. Therefore, the Jews’ responsibility for the leaven renders its legal status as if it belonged to them. However, according to the one who said: The legal status of an object that effects monetary loss is not like that of money, what can be said?

The Gemara answers: It is different here, as the verse said: “It shall not be found,” indicating that leaven may not be found in any place, even if there is only a token connection between the leaven and the Jew in whose property it is situated, and even if he is not required to pay for it if it is lost or stolen.

Some state a contrary version of the above discussion. This explanation works out well according to the one who said: The legal status of an object that effects monetary loss is not like that of money.