ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anabsi8 GIF version

Theorem anabsi8 524
Description: Absorption of antecedent into conjunction. (Contributed by NM, 26-Sep-1999.)
Hypothesis
Ref Expression
anabsi8.1 (𝜓 → ((𝜓𝜑) → 𝜒))
Assertion
Ref Expression
anabsi8 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsi8
StepHypRef Expression
1 anabsi8.1 . . 3 (𝜓 → ((𝜓𝜑) → 𝜒))
21anabsi5 521 . 2 ((𝜓𝜑) → 𝜒)
32ancoms 259 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator