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Theorem nesymir 2293
Description: Inference associated with nesym 2291. (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 2291 . 2  |-  ( B  =/=  A  <->  -.  A  =  B )
31, 2mpbir 144 1  |-  B  =/= 
A
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1285    =/= wne 2246
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-ne 2247
This theorem is referenced by: (None)
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