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Theorem exmidne 2833
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 2831 . 2 𝐴 = 𝐵𝐴𝐵)
21orri 390 1 (𝐴 = 𝐵𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wo 382   = wceq 1523  wne 2823
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 197  df-or 384  df-ne 2824
This theorem is referenced by:  elnn1uz2  11803  hashv01gt1  13173  numclwwlk3lemlem  27370  subfacp1lem6  31293  tendoeq2  36379  ax6e2ndeqVD  39459  ax6e2ndeqALT  39481
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