Is there a canonical database of theorems? Does a (public) database of theorems exist, as integer sequences are cataloged in the Online Encyclopedia of Integer Sequences (OEIS)?
 A: I might also add that ProofWiki is a community project to do such, complete with proofs.
A: The Metamath Proof Explorer "... has over 12,000 completely worked out proofs ..." [1] accessible via an indexed theorem list. [2]  Each theorem has a corresponding unique label.
The main Metamath page describes the project, the Metamath language, and programs and databases available for use. [3]  The Metamath proofs are mechanical, and may or may not be useful because of their tedium and lack of insight.
An alternative to Metamath is Ghilbert [4], which looks much nicer.  For example, contrast the Ghilbert proof of Euclid's Theorem [5] with the Metamath proof of infinitely many primes. [6]  Unfortunately, Ghilbert does not seem to have an indexed database of theorems like Metamath does.
Some ad hoc lists of theorems that do not include canonical identifiers are:


*

*https://en.wikipedia.org/wiki/List_of_theorems

*https://en.wikipedia.org/wiki/List_of_mathematical_proofs

*http://www.regentsprep.org/Regents/math/geometry/GPB/theorems.htm
The Cut the Knot and Wolfram Mathworld web sites are worth mentioning, if only because they have extensive collections of mathematical resources, many theorems included.
The following is a list of some related answers on math.SE. However, these answers did not address a canonical indexing of the theorems.


*

*The most common theorems taught in Abstract Algebra

*Does anybody know of a site that has a set of all theorems?
References:


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*[1] http://us.metamath.org/mpegif/mmset.html#overview

*[2] http://us.metamath.org/mpegif/mmtheorems.html (inline GIF images) and http://us.metamath.org/mpeuni/mmtheorems.html (unicode)

*[3] http://us.metamath.org/

*[4] http://ghilbert-app.appspot.com/

*[5] http://ghilbert-app.appspot.com/edit/peano/peano_thms.gh/euclidthm

*[6] http://us.metamath.org/mpegif/mmtheorems99.html#mm9884s
