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Theorem nf4 1753
Description: Alternate definition of non-freeness. This definition uses only primitive symbols. (Contributed by BJ, 16-Sep-2021.)
Assertion
Ref Expression
nf4 (Ⅎ𝑥𝜑 ↔ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ 𝜑))

Proof of Theorem nf4
StepHypRef Expression
1 nf3 1752 . 2 (Ⅎ𝑥𝜑 ↔ (∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑))
2 df-or 384 . 2 ((∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑) ↔ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ 𝜑))
31, 2bitri 264 1 (Ⅎ𝑥𝜑 ↔ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wo 382  wal 1521  wnf 1748
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 384  df-ex 1745  df-nf 1750
This theorem is referenced by:  nfimdOLDOLD  1864
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