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Theorem exmidne 2581
Description: Excluded middle with equality and inequality. (Contributed by NM, 3-Feb-2012.)
Assertion
Ref Expression
exmidne  |-  ( A  =  B  \/  A  =/=  B )

Proof of Theorem exmidne
StepHypRef Expression
1 exmid 405 . 2  |-  ( A  =  B  \/  -.  A  =  B )
2 df-ne 2577 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
32orbi2i 506 . 2  |-  ( ( A  =  B  \/  A  =/=  B )  <->  ( A  =  B  \/  -.  A  =  B )
)
41, 3mpbir 201 1  |-  ( A  =  B  \/  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 358    = wceq 1649    =/= wne 2575
This theorem is referenced by:  elnn1uz2  10516  hashv01gt1  11592  subfacp1lem6  24832  a9e2ndeqVD  28739  a9e2ndeqALT  28762  tendoeq2  31268
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-or 360  df-ne 2577
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