Theorem 2rexbidv

Description: Formula-building rule for restricted existential quantifiers (deduction form). (Contributed by NM, 28-Jan-2006)

	Ref	Expression
Hypothesis	2rexbidv.1	|- ( ph -> ( ps <-> ch ) )
Assertion	2rexbidv	|- ( 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		2rexbidv.1	|- ( ph -> ( ps <-> ch ) )
2	1	rexbidv	|- ( ph -> ( E. y e. B ps <-> E. y e. B ch ) )
3	2	rexbidv	|- ( ph -> ( E. x e. A E. y e. B ps <-> E. x e. A E. y e. B ch ) )