Theorem anabss3 796

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)

Hypothesis

Ref	Expression
anabss3.1	|- (((ph /\ ps) /\ ps) -> ch)

Assertion

Ref	Expression
anabss3	|- ((ph /\ ps) -> ch)

Proof of Theorem anabss3

Step	Hyp	Ref	Expression
1		anabss3.1	. . 3 |- (((ph /\ ps) /\ ps) -> ch)
2	1	anasss 628	. 2 |- ((ph /\ (ps /\ ps)) -> ch)
3	2	anabsan2 795	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:  3anidm23  1241