Theorem anabsan2 795

Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004.)

Hypothesis

Ref	Expression
anabsan2.1	|- ((ph /\ (ps /\ ps)) -> ch)

Assertion

Ref	Expression
anabsan2	|- ((ph /\ ps) -> ch)

Proof of Theorem anabsan2

Step	Hyp	Ref	Expression
1		anabsan2.1	. . 3 |- ((ph /\ (ps /\ ps)) -> ch)
2	1	an12s 776	. 2 |- ((ps /\ (ph /\ ps)) -> ch)
3	2	anabss7 794	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:  anabss3  796  anandirs  804