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Theorem nelir 2353
Description: Inference associated with df-nel 2351. (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 2351 . 2 (𝐴𝐵 ↔ ¬ 𝐴𝐵)
31, 2mpbir 144 1 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wcel 1438  wnel 2350
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-nel 2351
This theorem is referenced by:  prneli  3466  snnex  4262  ruv  4356  pnfnre  7508  mnfnre  7509  sqrt2irr  11234
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