For the source text click/tap here: Yevamot 89
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The Gemara on our daf suggests that we find a case of this in the first Mishnah of our perek. The Mishnah teaches that in a case where a man travels overseas and is reported dead, and the widow remarries based on the permission that she gets from the bet din, should the husband reappear, she is forbidden to them both, and both husbands must write her a get (a divorce). Furthermore, children that she has with either of these men will be considered mamzerim – children born from an adulterous relationship.
There are differences, however. It is clear that any child born from the second husband is a mamzer, since he was living with a married woman – albeit based on misinformation. Future children who are born from the first husband, however, should not be considered mamzerim – after all, the woman did not engage in forbidden relations on purpose.
Thus, the ruling that these children are mamzerim is only rabbinic.
The Gemara on our daf argues that declaring someone to be a mamzer when this is not true on a Torah level is effectively giving the Sages power to uproot a Biblical law.
We explore the power of the Beit Din including in modern states where church and state separate religious law such as in the UK and States and how this plays out beyond family and ritual law.