I hate to keep going with the big lists, but the question about one-sentence summaries of topics/areas spurred this question...and I just can't help myself!
Definition (Fraleigh): A proof synopsis is a one or two sentence synopsis of a proof, explaining the idea of the proof without all the details and computations.
My question is this:
What is your favorite proof synopsis of a theorem we all should know?
(I'm sorry, I'll do my time in big-list hell...)