Theorem ralimdvv

Description: Deduction doubly quantifying both antecedent and consequent. (Contributed by Scott Fenton, 2-Mar-2025)

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

Proof

Step	Hyp	Ref	Expression
1		ralimdvv.1	|- ( ph -> ( ps -> ch ) )
2	1	adantr	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> ( ps -> ch ) )
3	2	ralimdvva	|- ( ph -> ( A. x e. A A. y e. B ps -> A. x e. A A. y e. B ch ) )