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Metamath Proof Explorer

Theorem nfalh

Description: Version of nfal with an 'h' hypothesis, avoiding ax-12 . (Contributed by SN, 11-Feb-2026)

		Ref	Expression
	Hypothesis	nfalh.1	$⊢ φ \to \forall x φ$
	Assertion	nfalh	$⊢ Ⅎ x \forall y φ$

Step	Hyp	Ref	Expression
1		nfalh.1	$⊢ φ \to \forall x φ$
2	1	hbal	$⊢ \forall y φ \to \forall x \forall y φ$
3	2	nf5i	$⊢ Ⅎ x \forall y φ$