Theorem nftht 1792

Description: Closed form of nfth 1801. (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 1790	1 ⊢ (∀𝑥𝜑 → Ⅎ𝑥𝜑)

Syntax hints:   → wi 4  ∀wal 1538  ∃wex 1779  Ⅎwnf 1783

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 207  df-nf 1784

This theorem is referenced by:  nfth  1801  emptynf  1909  nfim1  2200  wl-nfeqfb  37559