For the source text click/tap here: Chullin 82
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We have learned above (see daf 78) that the Torah forbids the slaughter of an animal whose parent was killed on that day. Similarly, if the offspring was killed first, the parent cannot be slaughtered on that day (oto ve-et beno – see Vayikra 22:28).
The Mishna on our daf teaches that if mother and offspring were sold on the same day, the person who made the first purchase has the right to slaughter his animal first on that day, precluding the second from slaughtering. If, however, the person who made the second purchase went ahead and slaughtered his animal first, he has successfully claimed the right to do so and the other purchaser may not slaughter the animal that he purchased that day.