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Theorem eqid1 30270
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 261 . 2 (𝑥𝐴𝑥𝐴)
21eqriv 2725 1 𝐴 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534  wcel 2099
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1775  df-cleq 2720
This theorem is referenced by: (None)
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