Theorem ancomsd 256

Description: Deduction commuting conjunction in antecedent. (Contributed by NM, 12-Dec-2004.)

Hypothesis

Ref	Expression
ancomsd.1	|- ( ph -> ( ( ps /\ ch ) -> th ) )

Assertion

Ref	Expression
ancomsd	|- ( ph -> ( ( ch /\ ps ) -> th ) )

Proof of Theorem ancomsd

Step	Hyp	Ref	Expression
1		ancom 253	. 2 |- ( ( ch /\ ps ) <-> ( ps /\ ch ) )
2		ancomsd.1	. 2 |- ( ph -> ( ( ps /\ ch ) -> th ) )
3	1, 2	syl5bi 141	1 |- ( ph -> ( ( ch /\ ps ) -> th ) )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  sylan2d  278  mpand  405  anabsi6  514  ralxfrd  4194  rexxfrd  4195  poirr2  4717  smoel  5915  genprndl  6619  genprndu  6620  addcanprlemu  6713  leltadd  7442  lemul12b  7827  lbzbi  8551