The occurrence of an implication in finitely valid, intuitively improvable formulas of propositional logic

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.