Theorem anabsi8 588

Description: Absorption of antecedent into conjunction. (Contributed by NM, 26-Sep-1999.)

Hypothesis

Ref	Expression
anabsi8.1	|- ( ps -> ( ( ps /\ ph ) -> ch ) )

Assertion

Ref	Expression
anabsi8	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem anabsi8

Step	Hyp	Ref	Expression
1		anabsi8.1	. . 3 |- ( ps -> ( ( ps /\ ph ) -> ch ) )
2	1	anabsi5 585	. 2 |- ( ( ps /\ ph ) -> ch )
3	2	ancoms 268	1 |- ( ( ph /\ ps ) -> ch )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  subuhgr  16513  subupgr  16514  subumgr  16515  subusgr  16516