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Theorem nelir 2445
Description: Inference associated with df-nel 2443. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
nelir.1 ¬ 𝐴𝐵
Assertion
Ref Expression
nelir 𝐴𝐵

Proof of Theorem nelir
StepHypRef Expression
1 nelir.1 . 2 ¬ 𝐴𝐵
2 df-nel 2443 . 2 (𝐴𝐵 ↔ ¬ 𝐴𝐵)
31, 2mpbir 146 1 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wcel 2148  wnel 2442
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-nel 2443
This theorem is referenced by:  prneli  3617  snnex  4448  ruv  4549  pnfnre  7998  mnfnre  7999  eirr  11785  sqrt2irr  12161  topnex  13556
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