ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nelir GIF version

Theorem nelir 2458
Description: Inference associated with df-nel 2456. (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 2456 . 2 (𝐴𝐵 ↔ ¬ 𝐴𝐵)
31, 2mpbir 146 1 𝐴𝐵
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wcel 2160  wnel 2455
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-nel 2456
This theorem is referenced by:  prneli  3632  snnex  4466  ruv  4567  pnfnre  8028  mnfnre  8029  eirr  11817  sqrt2irr  12193  topnex  14038
  Copyright terms: Public domain W3C validator