Deep theorem with trivial proof 
It is the snobbishness of the young to suppose that a theorem is trivial because the proof is trivial.
-- Henry Whitehead

I have been awestruck by the beauty of this quote.
What is in your opinion a good contender to exemplefy the meaning intended by Whitehead?
Off the top of my head I am thinking of Langrange's theorem in Group Theory, which is rather simple to prove but provides a very useful insight.

The fundamental theorem of arithmetic.
The proof is generally shown to freshmen as an application of induction.
