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Theorem 19.9dOLD 2365
 Description: Obsolete proof of 19.9d 2225 as of 6-Oct-2021. (Contributed by NM, 14-May-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) Revised to shorten other proofs. (Revised by Wolf Lammen, 14-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.9dOLD.1 (𝜓 → Ⅎ𝑥𝜑)
Assertion
Ref Expression
19.9dOLD (𝜓 → (∃𝑥𝜑𝜑))

Proof of Theorem 19.9dOLD
StepHypRef Expression
1 19.9dOLD.1 . . 3 (𝜓 → Ⅎ𝑥𝜑)
2 df-nfOLD 1869 . . 3 (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
31, 2sylib 208 . 2 (𝜓 → ∀𝑥(𝜑 → ∀𝑥𝜑))
4 19.9ht 2308 . 2 (∀𝑥(𝜑 → ∀𝑥𝜑) → (∃𝑥𝜑𝜑))
53, 4syl 17 1 (𝜓 → (∃𝑥𝜑𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1629  ∃wex 1852  ℲwnfOLD 1857 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203 This theorem depends on definitions:  df-bi 197  df-ex 1853  df-nfOLD 1869 This theorem is referenced by:  19.9tOLD  2366
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