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Theorem nesymi 2266
Description: Inference associated with nesym 2265. (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 2265 . 2 (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)
31, 2mpbi 137 1 ¬ 𝐵 = 𝐴
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   = wceq 1259  wne 2220
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-ne 2221
This theorem is referenced by:  frec0g  6014  xrltnr  8802  nltmnf  8810
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