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Theorem 19.9t 2227
Description: A closed version of 19.9 2228. (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 2225 . 2 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
3 19.8a 2206 . 2 (𝜑 → ∃𝑥𝜑)
42, 3impbid1 215 1 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wex 1852  wnf 1856
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-12 2203
This theorem depends on definitions:  df-bi 197  df-ex 1853  df-nf 1858
This theorem is referenced by:  19.9  2228  19.21t  2229  19.21tOLDOLD  2230  spimt  2415  sbft  2526  vtoclegft  3431  bj-cbv3tb  33048  bj-spimtv  33055  bj-sbftv  33099  bj-equsal1t  33144  bj-19.21t  33152  19.9alt  34774
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