Theorem anabsi6 570

Description: Absorption of antecedent into conjunction. (Contributed by NM, 14-Aug-2000.)

Hypothesis

Ref	Expression
anabsi6.1	|- ( ph -> ( ( ps /\ ph ) -> ch ) )

Assertion

Ref	Expression
anabsi6	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem anabsi6

Step	Hyp	Ref	Expression
1		anabsi6.1	. . 3 |- ( ph -> ( ( ps /\ ph ) -> ch ) )
2	1	ancomsd 267	. 2 |- ( ph -> ( ( ph /\ ps ) -> ch ) )
3	2	anabsi5 569	1 |- ( ( ph /\ ps ) -> ch )

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:  anabsi7  571