Theorem ancomd 263

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 262	. 2 |- ( ( ps /\ ch ) <-> ( ch /\ ps ) )
3	1, 2	sylib 120	1 |- ( ph -> ( ch /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  elres  4664  relbrcnvg  4724  fvelrnb  5242  relelec  6169  prcdnql  6674  1idpru  6781  gt0srpr  6925  dvdsdivcl  10250  nn0ehalf  10303  nn0oddm1d2  10309  nnoddm1d2  10310  coprmgcdb  10470  divgcdcoprm0  10483  divgcdcoprmex  10484  cncongr1  10485