Theorem exrot4

Description: Rotate existential quantifiers twice. (Contributed by NM, 9-Mar-1995)

	Ref	Expression
Assertion	exrot4	$$⊢\exists x\exists y\exists z\exists w\phi \leftrightarrow \exists z\exists w\exists x\exists y\phi$$

Proof

Step	Hyp	Ref	Expression
1		excom13	$$⊢\exists y\exists z\exists w\phi \leftrightarrow \exists w\exists z\exists y\phi$$
2	1	exbii	$$⊢\exists x\exists y\exists z\exists w\phi \leftrightarrow \exists x\exists w\exists z\exists y\phi$$
3		excom13	$$⊢\exists x\exists w\exists z\exists y\phi \leftrightarrow \exists z\exists w\exists x\exists y\phi$$
4	2 3	bitri	$$⊢\exists x\exists y\exists z\exists w\phi \leftrightarrow \exists z\exists w\exists x\exists y\phi$$