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Theorem nelir 2294
Description: Inference associated with df-nel 2204. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
nelir.1 ¬ A B
Assertion
Ref Expression
nelir AB

Proof of Theorem nelir
StepHypRef Expression
1 nelir.1 . 2 ¬ A B
2 df-nel 2204 . 2 (AB ↔ ¬ A B)
31, 2mpbir 134 1 AB
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wcel 1390  wnel 2202
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-nel 2204
This theorem is referenced by:  snnex  4147  ruv  4228  pnfnre  6844  mnfnre  6845
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