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Theorem nfan1OLDOLD 2184
 Description: Obsolete version of nfan1 2183 as of 7-Jul-2022. (Contributed by Mario Carneiro, 3-Oct-2016.) df-nf 1828 changed. (Revised by Wolf Lammen, 18-Sep-2021.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfim1.1 𝑥𝜑
nfim1.2 (𝜑 → Ⅎ𝑥𝜓)
Assertion
Ref Expression
nfan1OLDOLD 𝑥(𝜑𝜓)

Proof of Theorem nfan1OLDOLD
StepHypRef Expression
1 df-an 387 . 2 ((𝜑𝜓) ↔ ¬ (𝜑 → ¬ 𝜓))
2 nfim1.1 . . . 4 𝑥𝜑
3 nfim1.2 . . . . 5 (𝜑 → Ⅎ𝑥𝜓)
4 nfnt 1901 . . . . 5 (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
53, 4syl 17 . . . 4 (𝜑 → Ⅎ𝑥 ¬ 𝜓)
62, 5nfim1 2182 . . 3 𝑥(𝜑 → ¬ 𝜓)
76nfn 1902 . 2 𝑥 ¬ (𝜑 → ¬ 𝜓)
81, 7nfxfr 1897 1 𝑥(𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 386  Ⅎwnf 1827 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-12 2163 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-ex 1824  df-nf 1828 This theorem is referenced by: (None)
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