Theorem nftht 1799

Description: Closed form of nfth 1808. (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 1797	1 ⊢ (∀𝑥𝜑 → Ⅎ𝑥𝜑)

Syntax hints:   → wi 4  ∀wal 1545  ∃wex 1786  Ⅎwnf 1790

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 208  df-nf 1791

This theorem is referenced by:  nfth  1808  emptynf  1916  nfim1  2211  wl-nfeqfb  37907