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I mean, if there exists a site that his function is to show and save theorems with their proofs?

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    Hey, nobody brought up [Math.StackExchange](http://math.stackexchange.com) and [Mathoverflow](http://mathoverflow.net/), yet?2012-05-25

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Here's a short list -- although it is indeed impossible to list all theorems.

Feel free to add any website/reference you find!