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 ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  sylan2d  294  mpand  433  anabsi6  586  ralxfrd  4608  rexxfrd  4609  poirr2  5180  smoel  6571  genprndl  7888  genprndu  7889  addcanprlemu  7982  leltadd  8775  lemul12b  9191  lbzbi  10016  dvdssub2  12602  odzdvds  13024  wlk1walkdom  16600