Daf Yomi Yevamot 27a: Rav Ashi's Induction Redux

A while back, I posted on Rav Ashi's proof by induction that if the yavama is one of a certain class of forbidden relatives, she exempts not only her rival, but also her rival's rival, etc., up to 100 times {and actually more -- it means ad infinitum}.

I wrote:

As I was preparing Rif Yomi, I noticed a proof by induction. In induction, you prove a base case, and then show that if something is true for n, it is true for n+1 as well (the inductive step).

In terms of rivals and rival's rivals, there are two approaches. A general derasha to cover all, or an induction. To cite the gemara:

{Yevamot 2b}

כיצד פוטרות צרותיהן היתה בתו או אחת מכל העריות האלו נשואה לאחיו ולו אשה אחרת ומת כשם שבתו פטורה כך צרתה פטורה
הלכה צרת בתו ונישאת לאחיו השני ולו אשה אחרת ומת כשם שצרת בתו פטורה כך צרת צרתה פטורה ואפי' הן מאה

Mishna:
How do they exempt their rivals? If his daughter, or any one of these forbidden relatives, was married to his brother, and he {=his brother} had another wife, and he {=his brother} died, just as his daughter is exempt {from requiring yibbum or chalitza from him}, so too her rival is exempt.
If the rival of his daughter went and married {via yibbum} his second brother, and he {=his second brother} had another wife, and then he {=his second brother} died, then just as the rival of his daughter is exempt, so it the rival of his rival exempt {from yibbum or chalitza with him}, and even if they {the levels} are 100.

{Yevamot 13a resumes}
Gemara:

מה"מ אמר רב יהודה אמר קרא לצרור התורה ריבתה צרות הרבה אצל ערוה אחת
רב אשי אמר צרת צרתה לא צריכא קרא סברא הוא צרה מאי טעמא אסירא דבמקום ערוה קיימא צרת צרתה נמי במקום צרה קיימא:

From where do we know these words?
Rav Yehuda said: The verse stated {Vayikra 18}: לצרור. The Torah thus includes many rivals by one forbidden relation.
Rav Ashi said: The rival of the rival does not require a verse. It is logic. A rival, what is the reason she is forbidden? Because she stands {together} in place of the forbidden relation. The rival of a rival also, she stands {together for yibbum} in place with the rival.

Thus, there is a general rule that if someone is a rival with someone forbidden, they are forbidden {and thus exempt from yibbum and chalitza as well}.

I saw something the other day from today's daf Yomi {when reading Rif on Yevamot 27a}, that continues in their vein. To cite from my translation of the Rif:

גופא אמר שמואל חלץ לאחיות לא נפטרו צרות לצרות נפטרו אחיות חלץ לבעלת הגט לא נפטרה צרה לצרה נפטרה בעלת הגט חלץ לבעלת מאמר לא נפטרה צרה לצרה נפטרה בעלת מאמר

ואקשינן מאי שנא חלץ לאחיות לא נפטרו צרות משום דהויא לה אחות אשה בזיקה חלץ לצרות נמי לא נפטרו אחיות דהויא לה צרת אחות אשה בזיקה
ופריק רב אשי משום דלא אלימא זיקה לשוויי לצרה כערוה
ופסקו רבוואתא הלכה כשמואל

To return to the main text. Shmuel said: If he performed chalitza to the sisters, the rivals are not exempt; to the rivals, the sisters are exempt; to the woman who received a bill of divorce, the rival is not exempt; to the rivals, the woman who received a bill of divorce is exempt. If he performed chalitza on a woman who was the recipient of maamar {Rabbinic betrothal prior to yibbum} the rival is not exempt; to the rival, the recipient of maamar is exempt.
And we ask: Why is the case of one who performs chalitza on sisters distinct in that the rivals are not exempt? Because she {each of them} is the sister of the wife {=achot ishto} through the bond. If he performs chalitza on the rivals as well, the sisters should not be exempt because they are the rivals of the sister of the wife via levirate bond!
And Rav Ashi resolves: Because the levirate bond is not strong enough to make the rival like the forbidden relation itself.

And the {post-Talmudic} Sages ruled that the halacha is like Shmuel.

Rav Ashi is consistent. Earlier he put forth the notion that learning the rival's rival is obvious, because the rival stands in place of the forbidden relation, to give us n+1 from any n. Here, he posits that this is not the case for the Rabbinic levirate bond (see Rashi), such that she does not stand in place of the forbidden relation. Thus, Rav Ashi leshitato.