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Theorem 19.9t 2189
Description: Closed form of 19.9 2190 and version of 19.3t 2185 with an existential quantifier. (Contributed by NM, 13-May-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (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 2187 . 2 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
3 19.8a 2166 . 2 (𝜑 → ∃𝑥𝜑)
42, 3impbid1 217 1 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  wex 1823  wnf 1827
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-12 2163
This theorem depends on definitions:  df-bi 199  df-ex 1824  df-nf 1828
This theorem is referenced by:  19.9  2190  19.21t  2191  sbftv  2245  spimtOLD  2351  sbft  2455  vtoclegft  3482  bj-cbv3tb  33307  bj-spimtv  33314  bj-equsal1t  33392  bj-19.21t  33400
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