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Theorem 19.9t 2202
 Description: Closed form of 19.9 2203 and version of 19.3t 2199 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 2201 . 2 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
3 19.8a 2178 . 2 (𝜑 → ∃𝑥𝜑)
42, 3impbid1 228 1 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209  ∃wex 1781  Ⅎwnf 1785 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2175 This theorem depends on definitions:  df-bi 210  df-ex 1782  df-nf 1786 This theorem is referenced by:  19.9  2203  19.21t  2204  sbft  2267  sbftALT  2569  vtoclegft  3530  bj-cbv3tb  34291  bj-spimtv  34298  bj-equsal1t  34327  bj-19.21t0  34335  19.9dev  39463
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