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Theorem 19.9t 2021
Description: A closed version of 19.9 2022. (Contributed by NM, 13-May-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) (Proof shortened by Wolf Lammen, 14-Jul-2020.)
Assertion
Ref Expression
19.9t (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))

Proof of Theorem 19.9t
StepHypRef Expression
1 id 22 . . 3 (Ⅎ𝑥𝜑 → Ⅎ𝑥𝜑)
2119.9d 2020 . 2 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
3 19.8a 1988 . 2 (𝜑 → ∃𝑥𝜑)
42, 3impbid1 213 1 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wex 1694  wnf 1698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-6 1838  ax-7 1885  ax-10 1966  ax-12 1983
This theorem depends on definitions:  df-bi 195  df-ex 1695  df-nf 1699
This theorem is referenced by:  19.9  2022  19.21t  2035  spimt  2144  sbft  2271  vtoclegft  3157  bj-cbv3tb  31736  bj-spimtv  31743  bj-sbftv  31793  bj-equsal1t  31842  bj-19.21t  31850  19.9alt  33164
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