The Gemara concludes: And the halakha is: If one slaughters from the incline of the thyroid cartilage and below in the direction of the windpipe, the slaughter is valid, and that is in accordance with the opinion that one who left part of the arytenoid cartilage has still performed a valid slaughter, as the arytenoids cartilage extends beyond this point.

The Gemara relates that Rav Naḥman deemed the slaughter valid in a case where one slaughtered from the incline of the thyroid cartilage and below. Rav Ḥanan bar Rav Ketina said to Rav Naḥman: In accordance with whose opinion is that ruling? It is neither in accordance with the opinion of the Rabbis nor in accordance with the opinion of Rabbi Yosei, son of Rabbi Yehuda, who both hold that if one cuts the windpipe above the large upper ring, the cricoid cartilage, the slaughter is not valid.

Rav Naḥman said to him: Neither do I know Ḥillek nor do I know Billek, i.e., I know the reason neither for this one’s opinion nor for that one’s opinion. I know the halakha, as Rabbi Ḥiyya bar Abba says that Rabbi Yoḥanan says, and some say that Rabbi Abba bar Zavda says that Rabbi Ḥanina says, and some say that Rabbi Ya’akov bar Idi says that Rabbi Yehoshua ben Levi says: From the incline of the thyroid cartilage and below, the slaughter is valid.

§ The Gemara returns to analyzing the baraita (18b): In a case where the knife is diverted from the place of slaughter above the ring, the slaughter is not valid. Rabbi Ḥanina ben Antigonus testified about a case where the knife is diverted from the place of slaughter above the ring that the slaughter is valid. And Rabbi Yehoshua ben Levi says: With regard to a case where the knife was diverted according to the opinion of the Rabbis cited in the mishna, the slaughter is valid according to the opinion of Rabbi Yosei, son of Rabbi Yehuda, who ruled that the slaughter is valid when the majority of the windpipe was cut within the large, upper ring.

And with regard to a case where the knife was diverted according to the opinion of Rabbi Yosei, son of Rabbi Yehuda, it is valid according to the opinion of Rabbi Ḥanina ben Antigonus, who ruled that even if a majority of the windpipe was cut outside the large upper ring, the slaughter is valid.

The Gemara objects: That is obvious. The Gemara explains: Lest you say that the statement of Rabbi Ḥanina ben Antigonus, who ruled that in a case where the knife is diverted from the place of slaughter above the ring it is valid, addresses the statement of the Rabbis and he agrees with the opinion of Rabbi Yosei, son of Rabbi Yehuda, that the slaughter is not valid when the majority of the windpipe was cut above the large upper ring, therefore, Rabbi Yehoshua ben Levi teaches us that this is not the case.

The Gemara objects: And say it is indeed so that Rabbi Ḥanina ben Antigonus agrees with Rabbi Yosei, son of Rabbi Yehuda. The Gemara responds: If so, the formulation of the baraita should have been: Rabbi Ḥanina ben Antigonus testified about it. Since the opinion of Rabbi Ḥanina ben Antigonus was introduced merely with the term: Testified, apparently he disagrees with all of the other opinions. The Gemara concludes: And the halakha is in accordance with the opinion of Rabbi Ḥanina ben Antigonus, as Rav Naḥman holds in accordance with his opinion.

§ The mishna cited a dispute between the Rabbis, who hold that in a case where one slaughtered within the large upper ring and did not leave a thread breadth over the entire surface of the ring, the slaughter is not valid, and Rabbi Yosei, son of Rabbi Yehuda, who hold that even if one left a thread breadth over a majority of the surface of the ring, the slaughter is valid. Apropos to that, Rav Huna said that Rav Asi says: The dispute is only in a case where one cut two-thirds of the windpipe within the ring and then diverted the knife upward toward the head of the animal and cut the remaining one-third, as the Rabbis hold that we require the entire slaughter to be performed within the large ring, and Rabbi Yosei, son of Rabbi Yehuda, holds: The halakhic status of its majority is like that of its entirety.

But if one diverted the knife upward toward the head of the animal, cut one-third of the windpipe, and then cut two-thirds within the ring, everyone agrees that the slaughter is not valid, as when the life left the animal, i.e., when the majority of the windpipe was cut, we require that the entire majority be cut by means of slaughter, and that is not so in this case.

Rav Ḥisda said to Rav Huna: On the contrary, let the Master say the opposite. The dispute is only in a case when one diverted the knife upward toward the head of the animal, cut one-third of the windpipe, and then cut two-thirds within the ring, as Rabbi Yosei, son of Rabbi Yehuda, holds that the slaughter is valid just as it is in the case where half the windpipe is deficient. In that case, once the slaughterer cuts any additional part of the windpipe, the slaughter is valid because the cut that rendered a majority of the windpipe slaughtered was performed properly. So too in this case, since the cut of the second third was performed properly, the slaughter is valid.

And the Rabbis hold that there, in the case of the deficient windpipe, the deficiency was in the place of proper slaughter, and therefore most of the life of the animal left in the proper place. Here, the first third was cut while the knife was diverted, and therefore most of the life of the animal did not leave in the place of proper slaughter.

But in a case where one cut two-thirds of the windpipe within the ring and then diverted the knife and cut the remaining one-third, everyone agrees that the slaughter is valid, as didn’t we learn in a mishna (27a): The halakhic status of the slaughter of the majority of one siman, the windpipe or the gullet, is like that of the slaughter of the entire siman itself?

Rav Yosef said to Rav Ḥisda: Who will say to us that with regard to the mishna there concerning the majority of one siman, Rabbi Yosei, son of Rabbi Yehuda, did not teach it? Perhaps Rabbi Yosei, son of Rabbi Yehuda, taught it, and the Rabbis disagree.

Abaye said to Rav Yosef: Is that to say that with regard to all principles that address majorities in general, Rabbi Yosei, son of Rabbi Yehuda, taught them? Rav Yosef said to him: I am speaking of the principle of majority with regard to slaughter, as we heard that the Rabbis disagree with him.

Some say that there is an alternative version of this discussion: Rav Huna said that Rav Asi says: The dispute is only in a case where one diverted the knife upward toward the head of the animal, cut one-third of the windpipe, and then cut two-thirds within the ring, as Rabbi Yosei, son of Rabbi Yehuda, holds that the slaughter is valid just as it is in the case where half the windpipe is deficient, and the Rabbis hold that there, in the case of the deficient windpipe, the deficiency was in the place of proper slaughter, but here, most of the life of the animal did not leave in the place of proper slaughter.

But in a case where one cut two-thirds of the windpipe within the ring and then diverted the knife and cut the remaining one-third, everyone agrees that the slaughter is valid, as didn’t we learn in a mishna (27a): The halakhic status of the slaughter of the majority of one siman, the windpipe or the gullet, is like that of the slaughter of the entire siman itself?

Rav Ḥisda objects to this: Who will say to us that with regard to the mishna there concerning the majority of one siman, Rabbi Yosei, son of Rabbi Yehuda, did not teach it? Perhaps Rabbi Yosei, son of Rabbi Yehuda, taught it, and the Rabbis disagree. Rav Yosef said to Rav Ḥisda: Is that to say that with regard to all principles that address majorities in general, Rabbi Yosei, son of Rabbi Yehuda, taught them? Rav Ḥisda said to him: I am speaking of the principle of majority with regard to slaughter, as we heard that the Rabbis disagree with him.

§ If one diverted the knife and cut one-third of the windpipe, and then cut one-third properly, and then diverted and cut the final one-third, Rav Huna says that Rav says: The slaughter is valid. Rav Yehuda says that Rav says: The animal is a tereifa, i.e., forbidden. Rav Huna says that Rav says: The slaughter is valid, as when the life left the animal, it was in the course of a valid slaughter that it left. Rav Yehuda says that Rav says: The animal is a tereifa, as we require a majority of the windpipe to be cut with valid slaughter,and that is not the case.

If one cut one-third of the windpipe properly, and then diverted the knife and cut one-third, and then cut the final one-third of the windpipe properly, Rav Yehuda says that Rav said: The slaughter is valid. When the Sages came and asked Rav Huna, he said to them: It is a tereifa. Rav Yehuda heard the ruling of Rav Huna, and he was angry. He said: I deem it a tereifa and he deems the slaughter valid, and I deem the slaughter valid and he deems it a tereifa. Rav Huna said: It is proper that he was angry. One reason is that he heard it from Rav and I did not hear it from Rav; and furthermore, isn’t there the majority of the siman that was cut with valid slaughter?

Rav Ḥisda said to Rav Huna: Do not retract your statement,