Theorem nfalh

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

	Ref	Expression
Hypothesis	nfalh.1	$$⊢\phi \to \forall x\phi$$
Assertion	nfalh	$$⊢Ⅎx\forall y\phi$$

Proof

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