Theorem anabss1 787

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)

Hypothesis

Ref	Expression
anabss1.1	|- (((ph /\ ps) /\ ph) -> ch)

Assertion

Ref	Expression
anabss1	|- ((ph /\ ps) -> ch)

Proof of Theorem anabss1

Step	Hyp	Ref	Expression
1		anabss1.1	. . 3 |- (((ph /\ ps) /\ ph) -> ch)
2	1	an32s 779	. 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:  anabss4  788