Why don’t first born sons of a bas Kohen need a pidyon haben?

Question

Per https://www.yeshiva.co/midrash/11477:

The obligation rests on the father of a boy who is the first-born of his mother and was born through natural delivery. If the father is a cohen or a levi, or if the mother is the daughter of a cohen or a levi, there is no mitzvah of pidyon haben. Since pidyon haben is dependent on the boy being the first-born of his mother, her pedigree is taken into consideration concerning whether there is a requirement to redeem her son (Bechoros 47a).

My understanding of the reasoning behind a pidyon haben is that the first born we’re originally supposed to serve with the Kohanim in the temple, but after the sin of the golden calf they were substituted by the Leviim. We redeem first borne from the Kohanim to purchase them back.

Per this understanding though, the first born of a bas Kohen born to an Israelite father should need to be redeemed, as due to his being a first born he should be serving, but due to his being an Israelite he wouldn’t be.

I see in Bechoros the rabbis use a drash to explain that this is not the case, but it doesn’t fit into my understanding of the ta’am of the mitzvah. So how does the halacha fit into the ta’am?

Answer 1

The Gemara Bechoros Daf 4a (Artscoll top of 4a3) say:

In Accordance with the interpretation of Mar the son of Rav Yosef in the name of Rava, who said: The verse describes a bechor as one that opens the womb²⁰. The Merciful One made bechor sanctity dependent on the opening of the womb²¹

²⁰ Scripture often refers to bechoros with this phrase. See for example *Numbers 3:12*

²¹ Mar the son of Rav Yosef relies on this exposition to explain why the Leviyah's first born is exempt even if she marries a Yisrael. The obligation of pidyon haben depends on the "opening of the womb", so when the womb that is opened is that of a Leviyah, he is exempt regardless of his paternal lineage (Rashi; see further, Reishis Bikkurim, Dvar Avraham vol. 3 7:8, Chazon Ish 16:6, Yad Binyamin)

The Gemara Bechoros daf 47a (Art Scroll 47a2) says

Rav Adda bar Ahavah said: If a Leviyah [i.e. daughter of a Levi] bore a firstborn son, her son is exempt from five selaim (pidyon haben)

The gemara then continues

Rather Rav Adda bar Ahavah refers to where she conceived from a Yisrael. But then how could he rule the son exempt from redemption? it is written by their families, according to their father's house ¹⁷

This teaches that children of Jewish Parents are tribally identified with their fathers ¹⁸

The gemarah then continues on 47a3:

Mar the son of Rav Yosef said in the name of Rava: In fact, Rav Adda bar Ahava refers to where [the Leviah] conceived from a Yisrael,

And as for your question that a child's geneology is determine by his father - which renders the child a Yisrael - the answer is that the there, with respect to a bechor for redemption, it is different, for the verse states: one that opens the womb. The Merciful One made redemption requirement** dependent on the opening of the womb** ²³

²³ Hence, although rhe child is in fact a Yisrael, he is nevertheless exempt from redemption, for the womb that he opened was that of a Leviah

Thus we see that a child is subject to Pidyon Haben only if both the father and the mother are from Yisrael. If the father is a kohen or Levi, then of course so is the child. If the father is a Yisrael but the mother's father is a Kohen or Levi, then the special circumstance of the pasuk applies.