Geodesic
The occurrence of an implication in finitely valid, intuitively improvable formulas of propositional logic
Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 383-390

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Kabakov has proved that for the finite validity (in Medvedev's sense) of intuitively unprovable propositional formulas it is necessary that an implication occur in the premise $\beta$ or else in the inference $\gamma$ of some subformula of the type $(\beta\to\gamma)$, and, consequently, that at least two implications be present. Here we prove that every finitely valid, intuitively unprovable formula contains the occurrence of an implication necessarily in the premise $\beta$ of some subformula of the form $(\beta\to\gamma)$ and we also present an example of a similar formula containing exactly two implications. 
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     author = {D. P. Skvortsov},
     title = {The occurrence of an implication in finitely valid, intuitively improvable formulas of propositional logic},
     journal = {Matemati\v{c}eskie zametki},
     pages = {383--390},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a9/}
}
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D. P. Skvortsov. The occurrence of an implication in finitely valid, intuitively improvable formulas of propositional logic. Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 383-390. http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a9/