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Theorem nfanOLD 1869
 Description: Obsolete proof of nfan 1868 as of 9-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 13-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
nfan.1 𝑥𝜑
nfan.2 𝑥𝜓
Assertion
Ref Expression
nfanOLD 𝑥(𝜑𝜓)

Proof of Theorem nfanOLD
StepHypRef Expression
1 df-an 385 . 2 ((𝜑𝜓) ↔ ¬ (𝜑 → ¬ 𝜓))
2 nfan.1 . . . 4 𝑥𝜑
3 nfan.2 . . . . 5 𝑥𝜓
43nfn 1824 . . . 4 𝑥 ¬ 𝜓
52, 4nfim 1865 . . 3 𝑥(𝜑 → ¬ 𝜓)
65nfn 1824 . 2 𝑥 ¬ (𝜑 → ¬ 𝜓)
71, 6nfxfr 1819 1 𝑥(𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 383  Ⅎwnf 1748 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1745  df-nf 1750 This theorem is referenced by: (None)
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