Theorem anabsi7 571

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)

Hypothesis

Ref	Expression
anabsi7.1	|- ( ps -> ( ( ph /\ ps ) -> ch ) )

Assertion

Ref	Expression
anabsi7	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem anabsi7

Step	Hyp	Ref	Expression
1		anabsi7.1	. . 3 |- ( ps -> ( ( ph /\ ps ) -> ch ) )
2	1	anabsi6 570	. 2 |- ( ( ps /\ ph ) -> ch )
3	2	ancoms 266	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  syl2an23an  1289  nelrdva  2933  elunii  3794  ordelord  4359  onsucuni2  4541  funfveu  5499  fvelrn  5616  phplem3g  6822  prdisj  7433  gcdmultiplez  11954  dvdssq  11964