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Theorem eqid1 21272
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
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 biid 227 . 2  |-  ( x  e.  A  <->  x  e.  A )
21eqriv 2363 1  |-  A  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1647    e. wcel 1715
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-cleq 2359
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