Theorem nftht 1824

Description: Closed form of nfth 1833. (Contributed by Wolf Lammen, 19-Aug-2018.) (Proof shortened by BJ, 16-Sep-2021.) (Proof shortened by Wolf Lammen, 3-Sep-2022.)

Assertion

Ref	Expression
nftht	⊢ (∀𝑥𝜑 → Ⅎ𝑥𝜑)

Proof of Theorem nftht

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (∀𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
2	1	nfd 1822	1 ⊢ (∀𝑥𝜑 → Ⅎ𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567  ∃wex 1811  Ⅎwnf 1815

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-nf 1816

This theorem is used by:  nfth  1833  emptynf  1941  nfim1  2235  wl-nfeqfb  38469