Theorem 2rexbidv

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

	Ref	Expression
Hypothesis	2ralbidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	2rexbidv	$$⊢\phi \to \left(\exists x\in A\exists y\in B\psi \leftrightarrow \exists x\in A\exists y\in B\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		2ralbidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	rexbidv	$$⊢\phi \to \left(\exists y\in B\psi \leftrightarrow \exists y\in B\chi \right)$$
3	2	rexbidv	$$⊢\phi \to \left(\exists x\in A\exists y\in B\psi \leftrightarrow \exists x\in A\exists y\in B\chi \right)$$