Theorem anabsi6 791

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 440	. 2 |- (ph -> ((ph /\ ps) -> ch))
3	2	anabsi5 790	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  anabsi7  792