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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  6397  djune  7076  omp1eomlem  7092  fodjum  7143  fodju0  7144  ismkvnex  7152  mkvprop  7155  omniwomnimkv  7164  3nelsucpw1  7232  xrltnr  9777  nltmnf  9786  xnn0xadd0  9865  pwle2  14630  nninfalllem1  14639  nninfall  14640  nninfsellemeq  14645  trirec0xor  14675
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