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

Theorem simpli 109
Description: Inference eliminating a conjunct. (Contributed by NM, 15-Jun-1994.)
Hypothesis
Ref Expression
simpli.1 (𝜑𝜓)
Assertion
Ref Expression
simpli 𝜑

Proof of Theorem simpli
StepHypRef Expression
1 simpli.1 . 2 (𝜑𝜓)
2 simpl 107 . 2 ((𝜑𝜓) → 𝜑)
31, 2ax-mp 7 1 𝜑
Colors of variables: wff set class
Syntax hints:  wa 102
This theorem was proved from axioms:  ax-mp 7  ax-ia1 104
This theorem is referenced by:  bi1  116  bi2  128  dfbi2  380  orc  666  pwundifss  4069  ssdomg  6347  negiso  8136  infrenegsupex  8799
  Copyright terms: Public domain W3C validator