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  5047  relbrcnvg  5113  fvelrnb  5689  relelec  6739  prcdnql  7694  1idpru  7801  gt0srpr  7958  fihashf1rn  11040  pfxccatin12  11304  prodmodclem3  12126  sinbnd  12303  cosbnd  12304  dvdsdivcl  12401  nn0ehalf  12454  nn0oddm1d2  12460  nnoddm1d2  12461  coprmgcdb  12650  divgcdcoprm0  12663  divgcdcoprmex  12664  cncongr1  12665  quscrng  14537  sincosq2sgn  15541  sincosq4sgn  15543