Theorem anabsi5 790

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 418	. 2 |- ((ph /\ (ph /\ ps)) -> ch)
3	2	anabss5 789	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 4   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  anabsi6  791  anabsi8  793  3anidm12  1239  rspce  2951