Theorem ancomd 267

Description: Commutation of conjuncts in consequent. (Contributed by Jeff Hankins, 14-Aug-2009.)

Hypothesis

Ref	Expression
ancomd.1	|- ( ph -> ( ps /\ ch ) )

Assertion

Ref	Expression
ancomd	|- ( ph -> ( ch /\ ps ) )

Proof of Theorem ancomd

Step	Hyp	Ref	Expression
1		ancomd.1	. 2 |- ( ph -> ( ps /\ ch ) )
2		ancom 266	. 2 |- ( ( ps /\ ch ) <-> ( ch /\ ps ) )
3	1, 2	sylib 122	1 |- ( ph -> ( ch /\ ps ) )

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:  elres  5049  relbrcnvg  5115  fvelrnb  5693  relelec  6744  prcdnql  7704  1idpru  7811  gt0srpr  7968  fihashf1rn  11051  pfxccatin12  11318  prodmodclem3  12154  sinbnd  12331  cosbnd  12332  dvdsdivcl  12429  nn0ehalf  12482  nn0oddm1d2  12488  nnoddm1d2  12489  coprmgcdb  12678  divgcdcoprm0  12691  divgcdcoprmex  12692  cncongr1  12693  quscrng  14566  sincosq2sgn  15570  sincosq4sgn  15572  subupgr  16143