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Theorem exmidne 2609
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 406 . 2  |-  ( A  =  B  \/  -.  A  =  B )
2 df-ne 2603 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
32orbi2i 507 . 2  |-  ( ( A  =  B  \/  A  =/=  B )  <->  ( A  =  B  \/  -.  A  =  B )
)
41, 3mpbir 202 1  |-  ( A  =  B  \/  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 359    = wceq 1653    =/= wne 2601
This theorem is referenced by:  elnn1uz2  10557  hashv01gt1  11634  subfacp1lem6  24876  a9e2ndeqVD  29095  a9e2ndeqALT  29117  tendoeq2  31645
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 179  df-or 361  df-ne 2603
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