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

Theorem ancomd 258
Description: Commutation of conjuncts in consequent. (Contributed by Jeff Hankins, 14-Aug-2009.)
Hypothesis
Ref Expression
ancomd.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
ancomd (𝜑 → (𝜒𝜓))

Proof of Theorem ancomd
StepHypRef Expression
1 ancomd.1 . 2 (𝜑 → (𝜓𝜒))
2 ancom 257 . 2 ((𝜓𝜒) ↔ (𝜒𝜓))
31, 2sylib 131 1 (𝜑 → (𝜒𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  elres  4671  relbrcnvg  4729  fvelrnb  5246  relelec  6174  prcdnql  6610  1idpru  6717  gt0srpr  6861  dvdsdivcl  10125  nn0ehalf  10178  nn0oddm1d2  10184  nnoddm1d2  10185
  Copyright terms: Public domain W3C validator