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Theorem nelir 2381
Description: Inference associated with df-nel 2379. (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 2379 . 2 (𝐴𝐵 ↔ ¬ 𝐴𝐵)
31, 2mpbir 145 1 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wcel 1463  wnel 2378
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-nel 2379
This theorem is referenced by:  prneli  3520  snnex  4337  ruv  4433  pnfnre  7771  mnfnre  7772  eirr  11392  sqrt2irr  11747  topnex  12161
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