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Theorem nesymi 2295
Description: Inference associated with nesym 2294. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
nesymi.1  |-  A  =/= 
B
Assertion
Ref Expression
nesymi  |-  -.  B  =  A

Proof of Theorem nesymi
StepHypRef Expression
1 nesymi.1 . 2  |-  A  =/= 
B
2 nesym 2294 . 2  |-  ( A  =/=  B  <->  -.  B  =  A )
31, 2mpbi 143 1  |-  -.  B  =  A
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1285    =/= wne 2249
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 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ne 2250
This theorem is referenced by:  frec0g  6066  xrltnr  8983  nltmnf  8991
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