An answer to this question advises that "If you can't prove it, then make it more complicated, then prove it". But my question is not when is proving the complicated one is easier, it is:
What are some famous cases when proving a generalization of a theorem is easier than proving the special case?
Usually, posts that contain very little information in the body get downvotes, but in this question, nothing is asked to be proved or solved, etc, so there are very less things to mention in this post.
Some users would say that this question should answer my question, but there are many reasons why it doesn't answer my question. An example of an answer can be:
Lindemann–Weierstrass theorem — if $α_1, ..., α_n$ are algebraic numbers that are linearly independent over the rational numbers ℚ, then $e^α_1, ..., e^α_n$ are algebraically independent over ℚ. The transcendence of $e$ and $\pi$ follows from this.
I don't know if the proof of this theorem is harder than the transcendence of e and pi, but this is a possible example.