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Theorem neir 2784
Description: Inference associated with df-ne 2781. (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 2781 . 2 (𝐴𝐵 ↔ ¬ 𝐴 = 𝐵)
31, 2mpbir 219 1 𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1474  wne 2779
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 195  df-ne 2781
This theorem is referenced by:  nesymir  2839  nsuceq0  5708  ax1ne0  9838  ine0  10317  nnunb  11138  nosgnn0i  30890  bj-pinftynminfty  32115
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