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 → ∀ 𝑥 𝜑 )
Assertion	nfalh	⊢ Ⅎ 𝑥 ∀ 𝑦 𝜑

Proof

Step	Hyp	Ref	Expression
1		nfalh.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
2	1	hbal	⊢ ( ∀ 𝑦 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜑 )
3	2	nf5i	⊢ Ⅎ 𝑥 ∀ 𝑦 𝜑