Theorem 4exbidv

Description: Formula-building rule for four existential quantifiers (deduction form). (Contributed by NM, 3-Aug-1995)

	Ref	Expression
Hypothesis	4exbidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	4exbidv	$$⊢\phi \to \left(\exists x\exists y\exists z\exists w\psi \leftrightarrow \exists x\exists y\exists z\exists w\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		4exbidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	2exbidv	$$⊢\phi \to \left(\exists z\exists w\psi \leftrightarrow \exists z\exists w\chi \right)$$
3	2	2exbidv	$$⊢\phi \to \left(\exists x\exists y\exists z\exists w\psi \leftrightarrow \exists x\exists y\exists z\exists w\chi \right)$$