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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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    http://planetmath.org/2012-05-25
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    _All_ theorems is a tall order. You might be interested in [ProofWiki](http://www.proofwiki.org/wiki/Main_Page).2012-05-25
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    [Metamath](http://us.metamath.org/) perhaps?2012-05-25
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    I mean not all, but a lot of them. Yes that is Im looking for. Thanks @DylanMoreland2012-05-25
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    @DylanMoreland, i thinks that U need your comment like answer. For i can put like this is the answer i needed. :)2012-05-25
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    What about sites corresponding to the automated proof-checkers?2012-05-25
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    This reminds me of "The Book" of Erdos, only less elegant.2012-05-25
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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!