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Theorem 19.9ht 2309
Description: A closed version of 19.9h 2276. (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 2134 . 2 (∀𝑥(𝜑 → ∀𝑥𝜑) → Ⅎ𝑥𝜑)
2119.9d 2192 1 (∀𝑥(𝜑 → ∀𝑥𝜑) → (∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1532  wex 1774
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-10 2130  ax-12 2167
This theorem depends on definitions:  df-bi 206  df-ex 1775  df-nf 1779
This theorem is referenced by:  bj-19.9htbi  36180
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