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Theorem exmidne 2452
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 404 . 2  |-  ( A  =  B  \/  -.  A  =  B )
2 df-ne 2448 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
32orbi2i 505 . 2  |-  ( ( A  =  B  \/  A  =/=  B )  <->  ( A  =  B  \/  -.  A  =  B )
)
41, 3mpbir 200 1  |-  ( A  =  B  \/  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 357    = wceq 1623    =/= wne 2446
This theorem is referenced by:  elnn1uz2  10294  ssnnssfz  23277  nnlogbexp  23406  subfacp1lem6  23716  a9e2ndeqVD  28685  a9e2ndeqALT  28708  tendoeq2  30963
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 177  df-or 359  df-ne 2448
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