Theorem anabss5 789

Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)

Hypothesis

Ref	Expression
anabss5.1	|- ((ph /\ (ph /\ ps)) -> ch)

Assertion

Ref	Expression
anabss5	|- ((ph /\ ps) -> ch)

Proof of Theorem anabss5

Step	Hyp	Ref	Expression
1		anabss5.1	. . 3 |- ((ph /\ (ph /\ ps)) -> ch)
2	1	anassrs 629	. 2 |- (((ph /\ ph) /\ ps) -> ch)
3	2	anabsan 786	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:  anabsi5  790