Theorem anabsi5 543

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 122	. 2 |- ( ( ph /\ ( ph /\ ps ) ) -> ch )
3	2	anabss5 542	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  anabsi6  544  anabsi8  546  3anidm12  1226  equsexd  1657  rspce  2696  phplem3g  6342  ltexprlemrl  6800  ltexprlemru  6802  dvdssq  10420