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Theorem nesymi 2393
Description: Inference associated with nesym 2392. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
nesymi.1 𝐴𝐵
Assertion
Ref Expression
nesymi ¬ 𝐵 = 𝐴

Proof of Theorem nesymi
StepHypRef Expression
1 nesymi.1 . 2 𝐴𝐵
2 nesym 2392 . 2 (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)
31, 2mpbi 145 1 ¬ 𝐵 = 𝐴
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   = wceq 1353  wne 2347
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-5 1447  ax-gen 1449  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-ne 2348
This theorem is referenced by:  frec0g  6400  djune  7079  omp1eomlem  7095  fodjum  7146  fodju0  7147  ismkvnex  7155  mkvprop  7158  omniwomnimkv  7167  3nelsucpw1  7235  xrltnr  9781  nltmnf  9790  xnn0xadd0  9869  fnpr2ob  12764  pwle2  14787  nninfalllem1  14796  nninfall  14797  nninfsellemeq  14802  trirec0xor  14832
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