Theorem 3exbidv

Description: Formula-building rule for three existential quantifiers (deduction form). (Contributed by NM, 1-May-1995)

	Ref	Expression
Hypothesis	3exbidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	3exbidv	$$⊢\phi \to \left(\exists x\exists y\exists z\psi \leftrightarrow \exists x\exists y\exists z\chi \right)$$

Proof

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