Theorem anabss3 864

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 679	. 2 |- ( ( ph /\ ( ps /\ ps ) ) -> ch )
3	2	anabsan2 863	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  3anidm23  1385  expclzlem  12884  plyrem  24060  anabss7p1  39014