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Theorem exmidne 2800
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 2798 . 2 𝐴 = 𝐵𝐴𝐵)
21orri 391 1 (𝐴 = 𝐵𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wo 383   = wceq 1480  wne 2790
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 385  df-ne 2791
This theorem is referenced by:  elnn1uz2  11709  hashv01gt1  13073  subfacp1lem6  30875  tendoeq2  35542  ax6e2ndeqVD  38628  ax6e2ndeqALT  38650
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