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Theorem nesymir 2998
Description: Inference associated with nesym 2996. (Contributed by BJ, 7-Jul-2018.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)
Hypothesis
Ref Expression
nesymir.1 ¬ 𝐴 = 𝐵
Assertion
Ref Expression
nesymir 𝐵𝐴

Proof of Theorem nesymir
StepHypRef Expression
1 nesymir.1 . . 3 ¬ 𝐴 = 𝐵
21neir 2942 . 2 𝐴𝐵
32necomi 2994 1 𝐵𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1540  wne 2939
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-9 2115  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1781  df-cleq 2723  df-ne 2940
This theorem is referenced by:  relowlpssretop  36711
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