English: “For their sake.” This teaches that the righteous protect the world.
On the daf / in context: The willingness of Hashem to spare an entire city for the sake of a small number of righteous people is the classic proof that the presence of tzaddikim shields the larger community.
Type of Learning
Derash on the verse (Bavli sugya) — not a formal named middah of the 13. The conditional promise is generalized into a principle of protection.
What Is Learned
The righteous protect the world; even a minority of fifty could have saved all of Sedom.