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Theorem exmidne 2665
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  =  B  \/  A  =/=  B )

Proof of Theorem exmidne
StepHypRef Expression
1 df-ne 2657 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
21biimpri 206 . 2  |-  ( -.  A  =  B  ->  A  =/=  B )
32orri 376 1  |-  ( A  =  B  \/  A  =/=  B )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    \/ wo 368    = wceq 1374    =/= wne 2655
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 185  df-or 370  df-ne 2657
This theorem is referenced by:  elnn1uz2  11147  hashv01gt1  12373  tgcgrextend  23597  tgbtwnexch2  23608  tgifscgr  23621  signstfvneq0  28155  subfacp1lem6  28255  ax6e2ndeqVD  32664  ax6e2ndeqALT  32686  tendoeq2  35445
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