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Theorem nesymir 2332
Description: Inference associated with nesym 2330. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
nesymir.1  |-  -.  A  =  B
Assertion
Ref Expression
nesymir  |-  B  =/= 
A

Proof of Theorem nesymir
StepHypRef Expression
1 nesymir.1 . 2  |-  -.  A  =  B
2 nesym 2330 . 2  |-  ( B  =/=  A  <->  -.  A  =  B )
31, 2mpbir 145 1  |-  B  =/= 
A
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1316    =/= wne 2285
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-5 1408  ax-gen 1410  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-cleq 2110  df-ne 2286
This theorem is referenced by: (None)
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