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Metamath Proof Explorer

Theorem nfe2

Description: An inner existential quantifier's variable is bound. (Contributed by SN, 11-Feb-2026)

		Ref	Expression
	Assertion	nfe2	$⊢ Ⅎ x \exists y \exists x φ$

Step	Hyp	Ref	Expression
1		excom	$⊢ \exists y \exists x φ \leftrightarrow \exists x \exists y φ$
2		nfe1	$⊢ Ⅎ x \exists x \exists y φ$
3	1 2	nfxfr	$⊢ Ⅎ x \exists y \exists x φ$