Theorem reximdvva

Description: Deduction doubly quantifying both antecedent and consequent, based on Theorem 19.22 of Margaris p. 90. (Contributed by AV, 5-Jan-2022)

	Ref	Expression
Hypothesis	reximdvva.1	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> ( ps -> ch ) )
Assertion	reximdvva	|- ( ph -> ( E. x e. A E. y e. B ps -> E. x e. A E. y e. B ch ) )

Proof

Step	Hyp	Ref	Expression
1		reximdvva.1	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> ( ps -> ch ) )
2	1	anassrs	|- ( ( ( ph /\ x e. A ) /\ y e. B ) -> ( ps -> ch ) )
3	2	reximdva	|- ( ( ph /\ x e. A ) -> ( E. y e. B ps -> E. y e. B ch ) )
4	3	reximdva	|- ( ph -> ( E. x e. A E. y e. B ps -> E. x e. A E. y e. B ch ) )