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Metamath Proof Explorer

Theorem nfale2

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

		Ref	Expression
	Assertion	nfale2	$⊢ Ⅎ x \forall y \exists x φ$

Step	Hyp	Ref	Expression
1		hbe1	$⊢ \exists x φ \to \forall x \exists x φ$
2	1	nfalh	$⊢ Ⅎ x \forall y \exists x φ$