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On the other hand, it is possible to say that when he retracted,
the Noda B’yehudah retracted from the first principle as well, namely
that yibum is contingent on being “without a child” at the time of
death and he will hold that even if a son is born after his father’s
death and the mother was not considered pregnant at the time of
her husband’s death, the son nevertheless exempts his mother from
chalitzah because the deceased is ultimately not lacking perpetuation
of his name and his name is not obliterated, and the situation at the
time of death is immaterial.

In his chiddushim, Rav Shkop (Yevamos, 33) writes that Tosfos’s
comments contradict the Noda B’yehudah’s first principle. The ge-
mara in Yevamos (35b) states, “Rabbi Yochanan said, ‘The chalitzah
of a pregnant woman is valid, because at the time of death he was
“without a child” and she therefore requires either chalitzah or yibum.’”
Tosfos (s.v. vehoh) ask: If so, when she did not do chalitzah and then
gave birth to a child, she should [still] require chalitzah because at
the moment of her husband’s death he was “without a child”? Tosfos
answer that when the child is viable we derive from “to perpetuate
his name” and from “his name shall not be obliterated” that a case
where his name is not obliterated is excluded. Thus, Rabbi Yochanan
also agrees that if the child is born viable, the mother is exempt from
chalitzah.

According to this the Noda B’yehudah’s first principle, namely
that if fertilization only takes place after the husband’s death the wife
requires chalitzah, is contradicted. According to Tosfos she is exempt
from chalitzah because ultimately his name is not obliterated and he
perpetuated his own name.

So, if we assume that the Noda B’yehudah in his conclusion re-
tracted his first principle completely because the deceased’s name is
not obliterated, in our case too, even if the artificial insemination was
done after his death, if it resulted in the birth of a viable child the
mother is exempt from chalitzah for in the final analysis the name
of the deceased is not obliterated, according to the poskim who rule
that a child born as a result of “bathtub conception” is considered his
father’s child.

54 1 Medical-Halachic Responsa of Rav Zilberstein