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Theorem nfntht2 1717
Description: Closed form of nfnth 1725. (Contributed by BJ, 16-Sep-2021.)
Assertion
Ref Expression
nfntht2 (∀𝑥 ¬ 𝜑 → Ⅎ𝑥𝜑)

Proof of Theorem nfntht2
StepHypRef Expression
1 olc 399 . 2 (∀𝑥 ¬ 𝜑 → (∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑))
2 nf3 1709 . 2 (Ⅎ𝑥𝜑 ↔ (∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑))
31, 2sylibr 224 1 (∀𝑥 ¬ 𝜑 → Ⅎ𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 383  wal 1478  wnf 1705
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 197  df-or 385  df-ex 1702  df-nf 1707
This theorem is referenced by:  nfnth  1725
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