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Theorem exmidne 2953
Description: Excluded middle with equality and inequality. (Contributed by NM, 3-Feb-2012.) (Proof shortened by Wolf Lammen, 17-Nov-2019.)
Assertion
Ref Expression
exmidne (𝐴 = 𝐵𝐴𝐵)

Proof of Theorem exmidne
StepHypRef Expression
1 neqne 2951 . 2 𝐴 = 𝐵𝐴𝐵)
21orri 860 1 (𝐴 = 𝐵𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wo 845   = wceq 1541  wne 2943
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 206  df-or 846  df-ne 2944
This theorem is referenced by:  elnn1uz2  12849  hashv01gt1  14244  numclwwlk3lem2lem  29274  hashxpe  31653  subfacp1lem6  33719  tendoeq2  39227  ax6e2ndeqVD  43172  ax6e2ndeqALT  43194
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