Theorem nfntht 1825

Description: Closed form of nfnth 1834. (Contributed by BJ, 16-Sep-2021.) (Proof shortened by Wolf Lammen, 4-Sep-2022.)

Assertion

Ref	Expression
nfntht	⊢ (¬ ∃𝑥𝜑 → Ⅎ𝑥𝜑)

Proof of Theorem nfntht

Step	Hyp	Ref	Expression
1		pm2.21 124	. 2 ⊢ (¬ ∃𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
2	1	nfd 1822	1 ⊢ (¬ ∃𝑥𝜑 → Ⅎ𝑥𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → 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:  nfntht2  1826