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  5041  relbrcnvg  5107  fvelrnb  5683  relelec  6730  prcdnql  7682  1idpru  7789  gt0srpr  7946  fihashf1rn  11022  pfxccatin12  11280  prodmodclem3  12101  sinbnd  12278  cosbnd  12279  dvdsdivcl  12376  nn0ehalf  12429  nn0oddm1d2  12435  nnoddm1d2  12436  coprmgcdb  12625  divgcdcoprm0  12638  divgcdcoprmex  12639  cncongr1  12640  quscrng  14512  sincosq2sgn  15516  sincosq4sgn  15518