Theorem anabsi5

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

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

Proof

Step	Hyp	Ref	Expression
1		anabsi5.1	|- ( ph -> ( ( ph /\ ps ) -> ch ) )
2		simpl	|- ( ( ph /\ ps ) -> ph )
3	2 1	mpcom	|- ( ( ph /\ ps ) -> ch )