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Theorem nesymir 2988
Description: Inference associated with nesym 2986. (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 2933 . 2 𝐴𝐵
32necomi 2984 1 𝐵𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1630  wne 2930
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1986  ax-6 2052  ax-7 2088  ax-9 2146  ax-ext 2738
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1852  df-cleq 2751  df-ne 2931
This theorem is referenced by:  relowlpssretop  33521
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