Theorem ancomsd 267

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 264	. 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-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  sylan2d  292  mpand  425  anabsi6  569  ralxfrd  4378  rexxfrd  4379  poirr2  4926  smoel  6190  genprndl  7322  genprndu  7323  addcanprlemu  7416  leltadd  8202  lemul12b  8612  lbzbi  9401  dvdssub2  11524