Kiddushin 12A

לא סלקא דעתך ⁠– דומיא דייעוד, מה ייעוד, אף על גב דאי בעי מייעד ואי בעי לא מייעד, כל היכא דלא מצי מייעד ⁠– לא הוו זבינא זביני, הכי נמי כל היכא דלא מצי[א] מיגרעא ⁠– לא הוו זבינא זביני.

The Talmud rejects this suggestion: This cannot enter your mind, as the halakha of deduction must be similar to the halakha of designation, i.e., the process by which a master designates his Hebrew female slave as a wife for him or his son (Exodus 21:8–9). Just as with designation, although the halakha is that if he desires, he may designate her and if he does not desire, he is not required to designate her, nevertheless anywhere that he cannot designate her, e.g., in a case where they are related and she is therefore forbidden to him, her sale is not a valid sale, so too here, with regard to her redemption, anywhere that she cannot deduct an amount from her purchase price, her sale is not a valid sale.

וקידושי אשה לבית שמאי נפקא להו מאמה העבריה: מה אמה העבריה בפרוטה לא מקניא, אף אשה בפרוטה לא מיקדשא.

The Talmud notes: And according to the opinion of Beit Shammai the mode of betrothal of a woman by money is derived from the case of a Hebrew female slave, as follows: Just as a Hebrew female slave cannot be acquired with one peruta, so too a woman cannot be betrothed with one peruta.

ואימא פלגא דדינר, ואימא שתי פרוטות! כיון דאפיקתיה מפרוטה ⁠– אוקמה אדינר.

The Talmud asks: Even if Beit Shammai derive their opinion from here, how does this prove that a woman can be betrothed only with a minimum of one dinar? But why not say she can be betrothed with half a dinar, or say that she can be betrothed with two perutot, as it is possible to fulfill the redemption of a Hebrew female slave if her sale was for either of these amounts? The Talmud answers: Since this comparison excludes betrothal with one peruta, as it indicates that a woman can be betrothed only with money of significant value, the rabbis established the minimum amount at one dinar, which is a coin of substantial value.