Theorem anabsan2 584

Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004.) (Revised by NM, 1-Jan-2013.)

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 565	. 2 |- ( ( ps /\ ( ph /\ ps ) ) -> ch )
3	2	anabss7 583	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  anabss3  585  anandirs  593  lmodvsdi  13867  lmodvsdir  13868  lmodvsass  13869  lss0cl  13925