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Theorem nfan1OLD 2224
 Description: Obsolete proof of nfan1 2056 as of 6-Oct-2021. (Contributed by Mario Carneiro, 3-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfan1OLD.1 𝑥𝜑
nfan1OLD.2 (𝜑 → Ⅎ𝑥𝜓)
Assertion
Ref Expression
nfan1OLD 𝑥(𝜑𝜓)

Proof of Theorem nfan1OLD
StepHypRef Expression
1 nfan1OLD.2 . . . . 5 (𝜑 → Ⅎ𝑥𝜓)
21nfrdOLD 2178 . . . 4 (𝜑 → (𝜓 → ∀𝑥𝜓))
32imdistani 722 . . 3 ((𝜑𝜓) → (𝜑 ∧ ∀𝑥𝜓))
4 nfan1OLD.1 . . . 4 𝑥𝜑
5419.28OLD 2223 . . 3 (∀𝑥(𝜑𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓))
63, 5sylibr 223 . 2 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
76nfiOLD 1725 1 𝑥(𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  ∀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-12 2034 This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nfOLD 1712 This theorem is referenced by:  nfanOLDOLD  2225
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