I was told that the fundamental group of a connected, compact, semisimple Lie group is finite, with the outline of a possible way to prove this fact.  Is there any source however that fleshes this out in detail / are there several ways to prove this fact?

Thanks!

(OK: this is known as Weyl's theorem, and I found a source in Knapp--the proof seems very different from the outline I was presented....)