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Theorem eqid1 27877
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.)

Ref Expression
eqid1 𝐴 = 𝐴

Proof of Theorem eqid1
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 biid 253 . 2 (𝑥𝐴𝑥𝐴)
21eqriv 2822 1 𝐴 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1656  wcel 2164
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-ext 2803
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1879  df-cleq 2818
This theorem is referenced by: (None)
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