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Theorem nesymi 2328
Description: Inference associated with nesym 2327. (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 2327 . 2  |-  ( A  =/=  B  <->  -.  B  =  A )
31, 2mpbi 144 1  |-  -.  B  =  A
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1314    =/= wne 2282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2283
This theorem is referenced by:  frec0g  6248  djune  6915  omp1eomlem  6931  fodjum  6968  fodju0  6969  ismkvnex  6979  mkvprop  6982  xrltnr  9459  nltmnf  9467  xnn0xadd0  9543  pwle2  12885  nninfalllem1  12895  nninfall  12896  nninfsellemeq  12902
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