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  11241  pfxccatin12  11519  prodmodclem3  12358  sinbnd  12535  cosbnd  12536  dvdsdivcl  12633  nn0ehalf  12686  nn0oddm1d2  12692  nnoddm1d2  12693  coprmgcdb  12882  divgcdcoprm0  12895  divgcdcoprmex  12896  cncongr1  12897  quscrng  14919  sincosq2sgn  15978  sincosq4sgn  15980  subupgr  16612