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Theorem eqid1 28396
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 264 . 2 (𝑥𝐴𝑥𝐴)
21eqriv 2735 1 𝐴 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wcel 2113
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019  ax-9 2123  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1787  df-cleq 2730
This theorem is referenced by: (None)
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