ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anabss3 GIF version

Theorem anabss3 519
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)
Hypothesis
Ref Expression
anabss3.1 (((𝜑𝜓) ∧ 𝜓) → 𝜒)
Assertion
Ref Expression
anabss3 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabss3
StepHypRef Expression
1 anabss3.1 . . 3 (((𝜑𝜓) ∧ 𝜓) → 𝜒)
21anasss 379 . 2 ((𝜑 ∧ (𝜓𝜓)) → 𝜒)
32anabsan2 518 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  3anidm23  1194  expclzaplem  9157
  Copyright terms: Public domain W3C validator