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Theorem nftht 1784
Description: Closed form of nfth 1793. (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
StepHypRef Expression
1 ax-1 6 . 2 (∀𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
21nfd 1782 1 (∀𝑥𝜑 → Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  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-nf 1776
This theorem is referenced by:  nfth  1793  emptynf  1901  nfim1  2189  wl-nfeqfb  34657
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