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Theorem nfntht 1801
Description: Closed form of nfnth 1810. (Contributed by BJ, 16-Sep-2021.) (Proof shortened by Wolf Lammen, 4-Sep-2022.)
Assertion
Ref Expression
nfntht (¬ ∃𝑥𝜑 → Ⅎ𝑥𝜑)

Proof of Theorem nfntht
StepHypRef Expression
1 pm2.21 123 . 2 (¬ ∃𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
21nfd 1798 1 (¬ ∃𝑥𝜑 → Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1541  wex 1787  wnf 1791
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 210  df-nf 1792
This theorem is referenced by:  nfntht2  1802
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