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

Theorem ancomsd 267
Description: Deduction commuting conjunction in antecedent. (Contributed by NM, 12-Dec-2004.)
Hypothesis
Ref Expression
ancomsd.1 (𝜑 → ((𝜓𝜒) → 𝜃))
Assertion
Ref Expression
ancomsd (𝜑 → ((𝜒𝜓) → 𝜃))

Proof of Theorem ancomsd
StepHypRef Expression
1 ancom 264 . 2 ((𝜒𝜓) ↔ (𝜓𝜒))
2 ancomsd.1 . 2 (𝜑 → ((𝜓𝜒) → 𝜃))
31, 2syl5bi 151 1 (𝜑 → ((𝜒𝜓) → 𝜃))
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:  sylan2d  292  mpand  425  anabsi6  554  ralxfrd  4353  rexxfrd  4354  poirr2  4901  smoel  6165  genprndl  7297  genprndu  7298  addcanprlemu  7391  leltadd  8177  lemul12b  8587  lbzbi  9376  dvdssub2  11462
  Copyright terms: Public domain W3C validator