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 ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  elres  5099  relbrcnvg  5166  fvelrnb  5750  relelec  6849  prcdnql  7851  1idpru  7958  gt0srpr  8115  fihashf1rn  11227  pfxccatin12  11505  prodmodclem3  12342  sinbnd  12519  cosbnd  12520  dvdsdivcl  12617  nn0ehalf  12670  nn0oddm1d2  12676  nnoddm1d2  12677  coprmgcdb  12866  divgcdcoprm0  12879  divgcdcoprmex  12880  cncongr1  12881  quscrng  14870  sincosq2sgn  15928  sincosq4sgn  15930  subupgr  16514