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Theorem neir 2978
Description: Inference associated with df-ne 2976. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
neir.1 ¬ 𝐴 = 𝐵
Assertion
Ref Expression
neir 𝐴𝐵

Proof of Theorem neir
StepHypRef Expression
1 neir.1 . 2 ¬ 𝐴 = 𝐵
2 df-ne 2976 . 2 (𝐴𝐵 ↔ ¬ 𝐴 = 𝐵)
31, 2mpbir 223 1 𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1653  wne 2975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 199  df-ne 2976
This theorem is referenced by:  nesymir  3033  nsuceq0  6025  ax1ne0  10273  ine0  10761  nnunb  11580  nosgnn0i  32329  bj-pinftynminfty  33617
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