Theorem ancomsd 266

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 263	. 2 |- ( ( ch /\ ps ) <-> ( ps /\ ch ) )
2		ancomsd.1	. 2 |- ( ph -> ( ( ps /\ ch ) -> th ) )
3	1, 2	syl5bi 151	1 |- ( ph -> ( ( ch /\ ps ) -> th ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  sylan2d  289  mpand  421  anabsi6  548  ralxfrd  4312  rexxfrd  4313  poirr2  4857  smoel  6103  genprndl  7177  genprndu  7178  addcanprlemu  7271  leltadd  8022  lemul12b  8419  lbzbi  9200  dvdssub2  11281