If someone had their first kid with a person who had children from a previous marriage, is that child a firstborn?
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The firstborn of one's mother is referred to in the Bible (Exodus 13:2) as one who "opens the womb" of his mother. Therefore, the firstborn of the father exclusively, although considered as a firstborn regarding his father's inheritance, is not considered as a firstborn regarding the requirement to be redeemed, as the mother's womb has already been opened by his half-sibling, the firstborn of his mother. Thus, the Shulchan Aruch rules that only a first born of the mother is required to be redeemed.
Kitzur Shulchan Aruch. Translated by Rabbi Avrohom Davis. Metsudah Publishers, 1996. P. 717