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Theorem 19.9ht 2335
Description: A closed version of 19.9h 2290. (Contributed by NM, 13-May-1993.) (Proof shortened by Wolf Lammen, 3-Mar-2018.)
Assertion
Ref Expression
19.9ht (∀𝑥(𝜑 → ∀𝑥𝜑) → (∃𝑥𝜑𝜑))

Proof of Theorem 19.9ht
StepHypRef Expression
1 nf5-1 2145 . 2 (∀𝑥(𝜑 → ∀𝑥𝜑) → Ⅎ𝑥𝜑)
2119.9d 2199 1 (∀𝑥(𝜑 → ∀𝑥𝜑) → (∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  wex 1776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-10 2141  ax-12 2173
This theorem depends on definitions:  df-bi 209  df-ex 1777  df-nf 1781
This theorem is referenced by:  bj-19.9htbi  34032
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