Theorem ancomsd 269

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 266	. 2 |- ( ( ch /\ ps ) <-> ( ps /\ ch ) )
2		ancomsd.1	. 2 |- ( ph -> ( ( ps /\ ch ) -> th ) )
3	1, 2	biimtrid 152	1 |- ( ph -> ( ( ch /\ ps ) -> th ) )

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:  sylan2d  294  mpand  429  anabsi6  582  ralxfrd  4583  rexxfrd  4584  poirr2  5155  smoel  6531  genprndl  7836  genprndu  7837  addcanprlemu  7930  leltadd  8721  lemul12b  9135  lbzbi  9948  dvdssub2  12521  odzdvds  12943  wlk1walkdom  16354