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I really need an example of some non-trivial proof (not related directly to set theory) that uses only logical symbols (no "words"). Thanks.

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 Principia Mathematica. Why do you "reallyneed" it, by the way? – Yemon Choi Sep 17 2011 at 0:07
This post seems similar (different "jc", by the way!) mathoverflow.net/questions/55458/… – jc Sep 17 2011 at 0:28

closed as off topic by Andy Putman, Felipe Voloch, Will Jagy, Joel David Hamkins, Qiaochu Yuan Sep 17 2011 at 0:40

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