Theorem ralimdv2

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 1-Feb-2005)

	Ref	Expression
Hypothesis	ralimdv2.1	|- ( ph -> ( ( x e. A -> ps ) -> ( x e. B -> ch ) ) )
Assertion	ralimdv2	|- ( ph -> ( A. x e. A ps -> A. x e. B ch ) )

Proof

Step	Hyp	Ref	Expression
1		ralimdv2.1	|- ( ph -> ( ( x e. A -> ps ) -> ( x e. B -> ch ) ) )
2	1	alimdv	|- ( ph -> ( A. x ( x e. A -> ps ) -> A. x ( x e. B -> ch ) ) )
3		df-ral	|- ( A. x e. A ps <-> A. x ( x e. A -> ps ) )
4		df-ral	|- ( A. x e. B ch <-> A. x ( x e. B -> ch ) )
5	2 3 4	3imtr4g	|- ( ph -> ( A. x e. A ps -> A. x e. B ch ) )