Theorem exrot3

Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995)

	Ref	Expression
Assertion	exrot3	$$⊢\exists x\exists y\exists z\phi \leftrightarrow \exists y\exists z\exists x\phi$$

Proof

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