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Theorem nfntht2 1786
Description: Closed form of nfnth 1794. (Contributed by BJ, 16-Sep-2021.) (Proof shortened by Wolf Lammen, 4-Sep-2022.)
Assertion
Ref Expression
nfntht2 (∀𝑥 ¬ 𝜑 → Ⅎ𝑥𝜑)

Proof of Theorem nfntht2
StepHypRef Expression
1 alnex 1773 . 2 (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑)
2 nfntht 1785 . 2 (¬ ∃𝑥𝜑 → Ⅎ𝑥𝜑)
31, 2sylbi 218 1 (∀𝑥 ¬ 𝜑 → Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1526  wex 1771  wnf 1775
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-ex 1772  df-nf 1776
This theorem is referenced by:  nfnth  1794
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