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Theorem nfntOLD 2197
 Description: Obsolete proof of nfnt 1767 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 28-Dec-2017.) (Revised by BJ, 24-Jul-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nfntOLD (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)

Proof of Theorem nfntOLD
StepHypRef Expression
1 nfnf1OLDOLD 2196 . 2 𝑥𝑥𝜑
2 df-nfOLD 1712 . . 3 (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
3 hbnt 2129 . . 3 (∀𝑥(𝜑 → ∀𝑥𝜑) → (¬ 𝜑 → ∀𝑥 ¬ 𝜑))
42, 3sylbi 206 . 2 (Ⅎ𝑥𝜑 → (¬ 𝜑 → ∀𝑥 ¬ 𝜑))
51, 4nfdOLD 2181 1 (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1473  ℲwnfOLD 1700 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701  df-nfOLD 1712 This theorem is referenced by:  nfnOLD  2198  nfndOLD  2199  19.23tOLD  2206
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