Theorem anabss1 855

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 846	. 2 |- ( ( ( ph /\ ph ) /\ ps ) -> ch )
3	2	anabsan 854	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:  anabss4  856  ordtri3or  5755  onfununi  7438  omordi  7646  oeoelem  7678  hashssdif  13200  nzss  38516  stirlinglem5  40295