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Theorem nelir 2705
Description: Inference associated with df-nel 2609. (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 2609 . 2 (𝐴𝐵 ↔ ¬ 𝐴𝐵)
31, 2mpbir 202 1 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wcel 1728  wnel 2607
This theorem is referenced by:  ru  3169  snnex  4748  ruv  7604  cardprc  7905  pnfnre  9165  mnfnre  9166  eirr  12842  sqr2irr  12886  zfbas  17966  aaliou3  20306
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 179  df-nel 2609
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