• Matzah of a כותי (אחזוק בדלא כתיבא) -  כל מצוה שהחזיקו בה כותים הרבה מדקדקין בה יותר מישראל 

The Gemara had taught that a כותי’s shechitah is permitted if the כותי eats a piece of it. Although the disqualifications of shechitah (שהייה, etc.) are not written in the Torah, since they established themselves as practicing these laws, they are considered reliable to follow them. The Gemara notes: ואחזוק ולא אחזוק בדלא כתיבא – and whether they can be established or cannot be established as reliable regarding a law which is not written is a machlokes Tannaim in a Baraisa: the Tanna Kamma says matzah baked by a כותי is permitted, and one can be יוצא the mitzvah of matzah with it (i.e., we can even assume it was guarded from becoming chametz לשם מצת מצוה). Rebbe Eliezer forbids their matzah, because we cannot rely on them that it did not become chametz. Rabban Shimon ben Gamliel says: כל מצוה שהחזיקו בה כותים – any mitzvah which the כותים have established for themselves, הרבה מדקדקין בה יותר מישראל – they are far more careful about them than Jews are. This appears identical to the Tanna Kamma, and the Gemara concludes that they disagree about דלא כתיבא ואחזיקו בה – something which is not written in the Torah, but they established for themselves. The Tanna Kamma holds they cannot be relied upon, and Rabba Shimon ben Gamliel holds they can.

• A מומר is לא שביק התירא ואכיל איסורא (and exchanges prohibited chametz for permitted chametz)

On the previous Daf, Rava said that a מומר לתיאבון may shecht לכתחלה if the knife was checked. The Gemara explains that when given the choice between eating היתר and eating איסור (i.e., shechting properly or not), לא שביק התירא ואכיל איסורא – he does not abandon the potential to eat permitted [food] and instead eat forbidden [food]. Still, we must check the knife, because מיטרח לא טרח – he will not bother to fix or replace a knife which is nicked. A Baraisa supports Rava: the chametz of עוברי עבירה – transgressors who do not destroy their chametz before Pesach, אחר הפסח מותר מיד – is permitted to others immediately after Pesach, מפני שהן מחליפין – because they exchange their forbidden chametz for the permitted chametz of non-Jews (although making this exchange is itself prohibited, the received chametz remains permitted to others). 

• Eating the shechitah of a מומר לעבודה זרה (proving that יהושפט ate from אחאב’s feast)

Rav Anan quoted Shmuel: ישראל מומר לעבודת כוכבים – a Jew who is a מומר regarding idolatry, מותר לאכול משחיטתו – it is permitted to eat from his shechitah, because we find that יהושפט מלך יהודה ate from אחאב’s feast. The passuk says: ויזבח לו אחאב צאן ובקר לרוב – and Achav slaughtered sheep and cattle for him in abundance, ולעם אשר עמו – and for the people who were with him, ויסיתהו לעלות אל רמות גלעד – and he enticed him to ascend to Ramos Gilad. We know that יהושפט partook of the feast, because the term "הסתה" refers to eating and drinking. The Gemara objects that perhaps יהושפט only drank, because the ordinary wine of idolators had not yet been forbidden, but did not eat, because a מומר לעבודת כוכבים is considered מומר לכל התורה כולה – a מומר for the entire Torah!? It answers that it is not fitting for a king to drink without eating; alternatively, the passuk implies that the “enticing” relates to the abovementioned shechitah.