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Theorem eqid1 29453
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 2734 1 𝐴 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wcel 2107
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-cleq 2729
This theorem is referenced by: (None)
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