Theorem alanimi

Description: Variant of al2imi with conjunctive antecedent. (Contributed by Andrew Salmon, 8-Jun-2011)

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

Proof

Step	Hyp	Ref	Expression
1		alanimi.1	|- ( ( ph /\ ps ) -> ch )
2	1	ex	|- ( ph -> ( ps -> ch ) )
3	2	al2imi	|- ( A. x ph -> ( A. x ps -> A. x ch ) )
4	3	imp	|- ( ( A. x ph /\ A. x ps ) -> A. x ch )