Mishnayos Chullin Perek 2 Mishnah 1

השוחט אחד בעוף – Because in that ab initio, it was necessary to slaughter two organs (i.e, both the windpipe and the esophagus) even with fowl, the Mishnah teaches "השוחט" –” he who ritually slaughters”, which implies that [only] one organ, for fowl [is required] de facto, but not ab initio. But two [organs are required] for cattle, ab initio, for how far does one go to slaughter [ritually]. Alternatively, because it was necessary to teach most of one [organ must be ritually slaughtered] like it, specifically de facto, for ab initio one must intend to slaughter the entire organ. And one [organ] in regard to fowl, fulfills one’s duty that it is fit, is from a Biblical verse, as it is written (Leviticus chapter 11, verse 46): “These are the instruction concerning animals, birds, all living creatures that move in the water [and all creatures that swarm on the earth],” the Bible attached [the category of] fowl between cattle and fish, to obligate [the ritual slaughter of] two organs, it is impossible that there was [already] an analogy made with fish; to exempt him [from doing any slaughtering] was impossible, since it was already compared to cattle. How was this accomplished? They (the Rabbis) made it ritually valid (for fowl) with one organ. And the act of ritual slaughter from the neck and and with two organs. Five things invalidate the act of ritual slaughter: שהייה–pausing during the act of slaughtering, דרסה–pressing the knife (adding muscular force to the cutting capacity of the knife, instead of passing the latter to and back (Hullin 20b), חלדה–pressing the life under cover; הגרמה–cutting the animal’s throat in a slanting direction (letting the knife slide beyond the space ritually designated for cutting); and עיקור–tearing loose the windpipe and esophagus before cutting, all of them are derived in the Gemara, regarding the esophagus and the windpipe and on the majority of one organ for fowl and on the majority of two organs for cattle.

עד שישחוט את הוורידים – like kinds of sinews upon the two sides of the windpipe, and regarding the foul alone, Rabbi Yehuda speaks, in order to remove its blood, since he roasted it entirely as one. And ritual slaughter, as stated by Rabbi Yehuda, not exactly, but rather that he should perforate the jugular vein prior to a skin–cover–membrane forms over the blood. For further blood will not come out, even though salting; but the Halakha does not follow Rabbi Yehuda.

רוב איד בעוף וכו' – And even though it is taught at the beginning of the Mishnah that most of one organ is like it, the Mishnah retracted here by teaching that one organ [is required] for fowl, etc., whether one is speaking about non-sacred meat or with meat dedicated for sacrificial purposes., for if we would teach only about non-sacred meat, I might say that it is enough for most [of one organ] because it was not for the blood that he needed it, but for the Holy Things (i.e. Sacrifices) for which the blood was necessary, it would not suffice to slaughter most of the organ; hence it comes to teach us that this was not the case.