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  4994  relbrcnvg  5060  fvelrnb  5625  relelec  6661  prcdnql  7596  1idpru  7703  gt0srpr  7860  fihashf1rn  10931  prodmodclem3  11828  sinbnd  12005  cosbnd  12006  dvdsdivcl  12103  nn0ehalf  12156  nn0oddm1d2  12162  nnoddm1d2  12163  coprmgcdb  12352  divgcdcoprm0  12365  divgcdcoprmex  12366  cncongr1  12367  quscrng  14237  sincosq2sgn  15241  sincosq4sgn  15243