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Theorem nesymir 3069
Description: Inference associated with nesym 3067. (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 3014 . 2 𝐴𝐵
32necomi 3065 1 𝐵𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1538  wne 3011
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-cleq 2815  df-ne 3012
This theorem is referenced by:  relowlpssretop  34742
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