Theorem ralimdvva

Description: Deduction doubly quantifying both antecedent and consequent, based on Theorem 19.20 of Margaris p. 90 ( alim ). (Contributed by AV, 27-Nov-2019)

	Ref	Expression
Hypothesis	ralimdvva.1	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> ( ps -> ch ) )
Assertion	ralimdvva	|- ( 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		ralimdvva.1	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> ( ps -> ch ) )
2	1	anassrs	|- ( ( ( ph /\ x e. A ) /\ y e. B ) -> ( ps -> ch ) )
3	2	ralimdva	|- ( ( ph /\ x e. A ) -> ( A. y e. B ps -> A. y e. B ch ) )
4	3	ralimdva	|- ( ph -> ( A. x e. A A. y e. B ps -> A. x e. A A. y e. B ch ) )