Theorem anabsi5 585

Description: Absorption of antecedent into conjunction. (Contributed by NM, 11-Jun-1995.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)

Hypothesis

Ref	Expression
anabsi5.1	|- ( ph -> ( ( ph /\ ps ) -> ch ) )

Assertion

Ref	Expression
anabsi5	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem anabsi5

Step	Hyp	Ref	Expression
1		anabsi5.1	. . 3 |- ( ph -> ( ( ph /\ ps ) -> ch ) )
2	1	imp 124	. 2 |- ( ( ph /\ ( ph /\ ps ) ) -> ch )
3	2	anabss5 584	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:  anabsi6  586  anabsi8  588  3anidm12  1336  equsexd  1782  rspce  2924  phplem3g  7157  ltexprlemrl  7977  ltexprlemru  7979  dvdssq  12808