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Theorem exmidne 2950
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 2948 . 2 𝐴 = 𝐵𝐴𝐵)
21orri 862 1 (𝐴 = 𝐵𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wo 847   = wceq 1543  wne 2940
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 210  df-or 848  df-ne 2941
This theorem is referenced by:  elnn1uz2  12521  hashv01gt1  13911  numclwwlk3lem2lem  28466  hashxpe  30847  subfacp1lem6  32860  tendoeq2  38525  ax6e2ndeqVD  42202  ax6e2ndeqALT  42224
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