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Theorem neir 2350
Description: Inference associated with df-ne 2348. (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 2348 . 2 (𝐴𝐵 ↔ ¬ 𝐴 = 𝐵)
31, 2mpbir 146 1 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   = wceq 1353  wne 2347
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-ne 2348
This theorem is referenced by:  exmidonfinlem  7191  pw1ne1  7227  pw1ne3  7228  sucpw1nel3  7231  ine0  8350  pwle2  14718
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