Theorem anabss5 857

Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994.) (Proof shortened by Wolf Lammen, 1-Jan-2013.)

Hypothesis

Ref	Expression
anabss5.1	|- ( ( ph /\ ( ph /\ ps ) ) -> ch )

Assertion

Ref	Expression
anabss5	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem anabss5

Step	Hyp	Ref	Expression
1		anabss5.1	. . 3 |- ( ( ph /\ ( ph /\ ps ) ) -> ch )
2	1	anassrs 680	. 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:  anabsi5  858  syl2an2r  876  mp3an2ani  1431  sq01  12986  faclbnd5  13085  hashssdif  13200  eqbrrdv2  34148  expgrowthi  38532  bccbc  38544  hoidmvlelem2  40810