If the kohen demands the first-born before the prescribed time, the owner does not need to provide it, because it seems that such a kohen would look too close to an employee of the owner — for taking care of the animal. Also, more on the question of giving terumah to the kohen when it does appear that he assists “on the threshing floor.” Note the fact of a rabbinic level of terumah as well as a Torah level. Also, delving into the meaning of “shanah be-shanah” – year by year, with regard to the first-born’s year, the calendar year, or perhaps the time of eating the sacrifice of the first-born.

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