Kiddushin, Chapter 4, Mishnah 11. This mishnah continues the topic discussed in the previous mishnah: a man who traveled overseas and returned from there with children - sometimes accompanied by a woman, and sometimes without her.
The first case - the woman is here before us:
The wording of the mishnah: "Ishah nasati bimdinas hayam, harei zu v'eilu baneha" - I married a woman overseas, and here she is with me, and these are her children. Regarding this the mishnah rules: "Meivi re'ayah la'ishah" - he must bring proof concerning the woman's lineage, for until now he has offered no proof about her at all, and therefore it falls upon him to demonstrate and bring testimony that she is a proper Jewish woman.
He is not required, however, to bring proof about the children, since - as we mentioned in the previous mishnah - we are dealing with a case where the children are clinging to her apron strings, so it is obvious that they are her children. Once her lineage has been established, the sons follow her as a matter of course.
The second case - the woman has died:
"Meisu, v'eilu baneha" - he married a woman overseas and she passed away, and now he claims that these are the children of that woman he married. In this case, "tzarich l'havi re'ayah al ha'ishah v'al baneha" - two proofs are required of him:
Proof about the woman: concerning the lineage of the woman who died, for we never saw this woman here at all.
Proof about the sons: that the children who are here with him are indeed the children of that woman whose lineage was properly established.
Once both proofs have been brought, the sons too are considered proper Jews.
To summarize: when the woman herself stands before us, proof of her lineage alone suffices, and the sons are drawn along after her automatically; but when she has died, there is no longer anyone to rely upon, and therefore a double proof is required - both concerning the woman's lineage and concerning the fact that these are her children.