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Theorem eqid1 20801
Description: Law of identity (reflexivity of class equality). Theorem 6.4 of [Quine] p. 41.

This law is thought to have originated with Aristotle (Metaphysics, Book VII, Part 17). It is one of the three axioms of Ayn Rand's philosophy (Atlas Shrugged, Part Three, Chapter VII). While some have proposed extending Rand's axiomatization to include Compassion and Kindness, others fear that such an extension may flirt with logical inconsistency. (Contributed by Stefan Allan, 1-Apr-2009.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion
Ref Expression
eqid1  |-  A  =  A

Proof of Theorem eqid1
StepHypRef Expression
1 biid 229 . 2  |-  ( x  e.  A  <->  x  e.  A )
21eqriv 2255 1  |-  A  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1619    e. wcel 1621
This theorem is referenced by:  bnj110  28022  lshpnelb  28424  hlhilocv  31400  hlhilhillem  31403
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1536  ax-ext 2239
This theorem depends on definitions:  df-bi 179  df-cleq 2251
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