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Theorem 19.9t 2204
Description: Closed form of 19.9 2205 and version of 19.3t 2201 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 2203 . 2 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
3 19.8a 2181 . 2 (𝜑 → ∃𝑥𝜑)
42, 3impbid1 225 1 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wex 1779  wnf 1783
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-12 2177
This theorem depends on definitions:  df-bi 207  df-ex 1780  df-nf 1784
This theorem is referenced by:  19.9  2205  19.21t  2206  sbft  2270  vtoclegftOLD  3589  bj-cbv3tb  36788  bj-spimtv  36795  bj-equsal1t  36823  bj-19.21t0  36831  19.9dev  42253
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