Theorem anabss7 517

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 19-Nov-2013.)

Hypothesis

Ref	Expression
anabss7.1	|- ( ( ps /\ ( ph /\ ps ) ) -> ch )

Assertion

Ref	Expression
anabss7	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem anabss7

Step	Hyp	Ref	Expression
1		anabss7.1	. . 3 |- ( ( ps /\ ( ph /\ ps ) ) -> ch )
2	1	anassrs 380	. 2 |- ( ( ( ps /\ ph ) /\ ps ) -> ch )
3	2	anabss4 511	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  anabsan2  518  funbrfv  5212