Theorem nfalh 42795

Description: Version of nfal 2354 with an 'h' hypothesis, avoiding ax-12 2211. (Contributed by SN, 11-Feb-2026.)

Hypothesis

Ref	Expression
nfalh.1	⊢ (𝜑 → ∀𝑥𝜑)

Assertion

Ref	Expression
nfalh	⊢ Ⅎ𝑥∀𝑦𝜑

Proof of Theorem nfalh

Step	Hyp	Ref	Expression
1		nfalh.1	. . 3 ⊢ (𝜑 → ∀𝑥𝜑)
2	1	hbal 2200	. 2 ⊢ (∀𝑦𝜑 → ∀𝑥∀𝑦𝜑)
3	2	nf5i 2179	1 ⊢ Ⅎ𝑥∀𝑦𝜑

Syntax hints:   → wi 4  ∀wal 1557  Ⅎwnf 1802

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-10 2174  ax-11 2190

This theorem depends on definitions:  df-bi 209  df-ex 1799  df-nf 1803

This theorem is referenced by:  nfale2  42797