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Metamath Proof Explorer

Theorem exrot3

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

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

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