Gemara

14b (Mishnah): In all places one may not sell to Nochrim large animals, calves and foals, healthy or lame;

R. Yehudah permits selling a lame animal;

Ben Beseira permits selling a horse.

15a - Opinion #1: The Isur to sell work animals is a decree, lest one rent or lend an animal to a Nochri.

Objection: One who rents or borrows an animal acquires it (for the agreed period of time)!

Opinion #2 (Rami brei d'R. Yeva): This is a decree, lest the Nochri want to test the animal;

Sometimes he buys an animal just before Shabbos, and wants to see how it carries burdens. The animal goes when it hears its owner's voice, and the owner transgresses making an animal work on Shabbos.

Rav Huna sold a cow to a Nochri. He explained 'I may assume that he bought it to eat it immediately.'

Rabah sold a donkey to someone suspected of selling to Nochrim. He explained 'he might sell to a Nochri, but he might sell to a Yisrael. Therefore, I may assume that he will sell to a Yisrael.'

Question (Beraisa): In a place where the custom is to not to sell small animals to Kusim (converts whi did not accept Divrei Chachamim), it is forbidden.

This is because they sell them to Nochrim. Rav Nachman taught that just like one may not sell to a Nochri, one may not sell to a Yisrael suspected of selling to Nochrim.

Rabah ran to retract the sale, but he was unable to catch the buyer.

16a - Question: May one sell a Shor Shel Petem (a fattened ox)?

R. Yehudah permits selling a lame animal, for it will never be proper to work, but a fattened ox will become proper if left for a while!

Chachamim forbid a lame animal, for it was not sold to be eaten (perhaps he will keep for children), but a fattened ox is to be eaten!

Answer: Rav Yehudah taught that Romi required Rebbi's house to give to them a fattened ox on their festivals. Rebbi gave huge bribes to weaken and eventually abolish this.

Suggestion: He bribed them to abolish it because it is forbidden, lest the Nochri keep the ox for a while.

Question: Will a fattened ever become suitable for work?

Answer (Rav Ashi): Yes! A fattener told me that if it is left to get thin again, it will work twice as good as a normal ox.

20b (Beraisa - R. Yehudah): We may sell to them an animal (that is usually bought for work) on condition to slaughter it, and he must slaughter it;

R. Meir says, we may sell to them only a slaughtered animal.

Rishonim

Rif (6a): The Halachah follows R. Meir, for the Stam Mishnah is like him.

Ran (5a DH v'Chulei): The Mishnah discusses Stam people, who presumably buy for plowing. Rav Huna sold to a butcher. Even though he buys also for plowing, we are lenient to assume that he buys for slaughter.

Ran (DH Kach): One may not sell to a Yisrael suspected to sell to Nochrim, lest the first seller transgress Lifnei Iver. Rav Huna was lenient, because it can be determined immediately that the buyer needs it for Heter, and he is particular that it not be used for work. If one buys to sell, and he does not care if he sells to a Yisrael or Nochri, we are not lenient to assume that he will sell else to a Yisrael.

Ran (DH Garsinan): The Gemara did not explicitly resolve the question of a Shor Shel Petem. Even though this is a mid'Rabanan law, the Rambam is stringent because Rav Ashi taught that a fattened ox that becomes thin again works twice as good as a normal ox. I.e. we may not assume that one buys it for slaughter. It seems that the Rif agrees, therefore, he omitted it from his Halachos.

Rambam (Hilchos Shabbos 20:4): Just like one may not sell (animals) to Nochrim, one may not sell to a Yisrael suspected of selling to Nochrim. One may sell a cow for slaughter, and he slaughters it in front of him. One may not sell Stam even a Shor Shel Petem, lest he keep it and work with it.

Magid Mishneh: The Rambam rules like R. Yehudah against R. Meir, for in Eruvin we say that we normally follow him against R. Meir. Rav Huna supports this. Even though the Meforshim explain that he sold to a butcher who buys for slaughter and for plowing, if the Halachah followed R. Meir, we would not be more lenient about selling to such a butcher than about selling to one who buys for slaughter and slaughters. Also, how could Rav Huna justify his sale?

Lechem Mishneh: What is the additional question from Rav Huna? It seems that even if you will say that we are more than lenient about a butcher than about one who buys to slaughter, why was Rav Huna lenient? 'I assume that he will slaughter it' suggests that this was his Heter, and not because he sold to a butcher.

Magid Mishneh: The Rif and Ramban rule like R. Meir, for the Stam Mishnah is like him. The Rashba permits selling to a butcher who buys for slaughter, even if he sometimes buys for plowing, or to a Nochri who is making a feast. We assume that he buys it for slaughter. This is astounding. Why are we more lenient about one whom we estimate that he intends to slaughter, than for one who buys on condition to slaughter and slaughters?!

Rosh (1:16): Rav Huna sold a cow to a Nochri. He assumed that he bought it to eat it immediately. Rashi says that the Mishnah forbids Tamei animals, or when the Nochri said that he intends to keep it. This is difficult, for the Mishnah mentions calves and young donkeys; presumably, both are the same (the Nochri need not say that he intends to keep it). The Rashbam explains in the name of Rashi that we are lenient about a cow, for it is not so common to work with them. The Mishnah forbids bulls, which are normally used for plowing. R. Tam disagrees, for Mishnayos connote that most plowing is with cows! Rather, we assume that all cattle are for eating. The Mishnah forbids selling Tamei work animals. Calves are different; we assume that he bought them to raise them for work, like young donkeys. The Gemara asks about Shor Shel Petem. This does not mean a fattened bull (for surely it is for eating, and it is permitted). Rather, it refers to selling an animal to be fattened. Since he must invest to fatten it, we are concerned lest he reconsider and work with it, like we are concerned about calves. Rav Hai Gaon says that if it seems that the Nochri intends to slaughter it, it is permitted, like Rav Huna did. The Ramban says that Rav Huna sold to a butcher. Rav Chisda thought to forbid, for most buy for plowing. The Gemara supported Rav Huna from a Mishnah that permits selling a plowing cow in Shemitah. The Yerushalmi says that all permit if one sells to a butcher, and all forbid if one sells to a sharecropper. Beis Hillel and Beis Shamai argue about one who sold to a middleman.

Poskim

Shulchan Aruch (YD 151:4): In every place one may not sell large animals to Nochrim or to Yisre'elim suspected of selling to Nochrim, unless it is through a wholesaler, or he knows that he buys it to slaughter it. Nowadays, the custom is to permit everything.

Taz (4): The Tur permits selling to a butcher, for he buys for slaughter. He forbids selling to a landowner, for he buys for plowing. The first law implies that one may not sell to a Stam person, and the latter law connotes that it is permitted! It seems that it depends on the person, to be lenient or stringent. I.e. we permit to a butcher and forbid to a landowner, regardless of what most buy for. Regarding a Stam person, it depends on what most buy for.