ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anabss7 GIF version

Theorem anabss7 517
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 19-Nov-2013.)
Hypothesis
Ref Expression
anabss7.1 ((𝜓 ∧ (𝜑𝜓)) → 𝜒)
Assertion
Ref Expression
anabss7 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabss7
StepHypRef Expression
1 anabss7.1 . . 3 ((𝜓 ∧ (𝜑𝜓)) → 𝜒)
21anassrs 380 . 2 (((𝜓𝜑) ∧ 𝜓) → 𝜒)
32anabss4 511 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:  anabsan2  518  funbrfv  5199
  Copyright terms: Public domain W3C validator