Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  eqid1 Structured version   Visualization version   GIF version

Theorem eqid1 26715
 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 250 . 2 (𝑥𝐴𝑥𝐴)
21eqriv 2607 1 𝐴 = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∈ wcel 1977 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-cleq 2603 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator