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Theorem nelir 2896
Description: Inference associated with df-nel 2894. (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 2894 . 2 (𝐴𝐵 ↔ ¬ 𝐴𝐵)
31, 2mpbir 221 1 𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 1987  wnel 2893
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 197  df-nel 2894
This theorem is referenced by:  ru  3421  prneli  4180  snnexOLD  6931  ruv  8467  ruALT  8468  cardprc  8766  pnfnre  10041  mnfnre  10042  wrdlndm  13276  eirr  14877  sqrt2irr  14922  lcmfnnval  15280  lcmf0  15290  zringndrg  19778  topnex  20740  zfbas  21640  aaliou3  24044  clwwlksn0  26807  xrge0iifcnv  29803  bj-0nel1  32640  bj-1nel0  32641  bj-0nelsngl  32659  fmtnoinf  40777  fmtno5nprm  40824  0nodd  41128  2nodd  41130  1neven  41250  2zrngnring  41270
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