ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anabsi7 GIF version

Theorem anabsi7 581
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)
Hypothesis
Ref Expression
anabsi7.1 (𝜓 → ((𝜑𝜓) → 𝜒))
Assertion
Ref Expression
anabsi7 ((𝜑𝜓) → 𝜒)

Proof of Theorem anabsi7
StepHypRef Expression
1 anabsi7.1 . . 3 (𝜓 → ((𝜑𝜓) → 𝜒))
21anabsi6 580 . 2 ((𝜓𝜑) → 𝜒)
32ancoms 268 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  syl2an23an  1299  nelrdva  2944  elunii  3812  ordelord  4378  onsucuni2  4560  funfveu  5524  fvelrn  5643  phplem3g  6850  prdisj  7479  gcdmultiplez  12002  dvdssq  12012
  Copyright terms: Public domain W3C validator