ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anabss5 GIF version

Theorem anabss5 550
Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)
Hypothesis
Ref Expression
anabss5.1 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
Assertion
Ref Expression
anabss5 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabss5
StepHypRef Expression
1 anabss5.1 . . 3 ((𝜑 ∧ (𝜑𝜓)) → 𝜒)
21anassrs 395 . 2 (((𝜑𝜑) ∧ 𝜓) → 𝜒)
32anabsan 547 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anabsi5  551  syl2an2r  567  mp3an2ani  1305
  Copyright terms: Public domain W3C validator