Bechoros Daf 3 בכורות דַף 3

The Gemara presents three opinions about an עכו"ם’s partnership in an animal which exempts it from bechor status: Rav Huna says אפילו אזנו – even if his partnership is only in its ear. Rav Nachman objected: ולימא ליה שקיל אזנך וזיל – but let [the Kohen] tell him, “Take your ear and go!” but the rest of the animal should be subject to בכורה!? Rav Chisda says the עכו"ם’s partnership must involve דבר שעושה אותו נבלה – something which [if removed] would make the animal a neveilah, and Rava says: דבר שעושה אותו טריפה – something which [if removed] would make the animal a tereifah. Rav holds טריפה אינה חיה – a tereifah cannot live, making such limbs essential, and Rav Chisda holds טריפה חיה. Rav Pappa says that just as Rav Huna exempts where an עכו"ם is a partner in the bechor’s ear (because it is lacking in "כל" בכור), he would also exempt partnership in the mother’s ear (because it is lacking in "כל מקנך"). Although נפלים – non-viable offspring are subject to bechor status (and must be buried), that is because there is no chullin portion mixed into them, but regarding שותפות with an idolator, כיון דעריבו בהו חולין – since there is chullin (the עכו"ם’s share) mixed into them, they are excluded from "כל" בכור.

A Mishnah teaches that if a female sheep bore a firstborn resembling a goat, or vice versa, it is exempt from bechor status, ואם יש בו מקצת סימנין – but if it has partial features like its mother, it has bechor status. Rebbe Yochanan says that although it is a bechor (and is given to a Kohen), its unusual appearance is a מום קבוע, and the Kohen may shecht it for his personal consumption, becauseכיון דאישתני הוה ליה מומא – since it mutated, [its mutation] is a blemish. Although a Mishnah already taught that פיו דומה כשל חזיר – [a bechor] whose mouth is similar to that of a pig is a מום, that is a mutation resembling a creature which is not subject to bechor, as opposed to a sheep resembling a goat. Although another Mishnah teaches that a bechor with one large eye or one small eye is a בעל מום, and “a large eye” refers to the eye size of a calf (which is subject to bechor), the Gemara explains that this מום may not be because of שינוי, but because it is "שרוע", an animal with limbs of unequal size.

Rav Mari bar Rachel would transfer ownership of the ears of his firstborn animals to an עכו"ם before they were born, to exempt them from bechor status. Still, he prohibited them for גיזה ועבודה – shearing and work and gave them to a Kohen, like an ordinary bechor. Ultimately, his flock died out, although his intent was to prevent תקלה – an inadvertent transgression (of גיזה or עבודה),משום דמפקע להו מקדושתייהו – because he removed them from they [bechor] sanctity. The Gemara objects that Rav Yehudah permits inflicting a מום on a bechor fetus before its birth to prevent its bechor status!? It answers that a מום only precludes it from קדושת מזבח (i.e., as a korban), but it still attains "קדושת כהן" – sanctity for the Kohen, i.e., the kedushah of a bechor which is a בעל מום, which is given to the Kohen, and cannot be shorn or worked. Alternatively, Rav Mari knew how to properly transact with an idolator (i.e., to receive money from him), but others observing him might make an ineffective transaction, leading to an inadvertent transgression.