 Solution

The unique readability theorem says that every propositional formula has exactly one of the following forms: a unique propositional variable; $\neg \psi$ for a unique logical formula $\psi$; or $(\psi \to \chi )$ for a unique ordered pair of logical formulas $(\psi ,\chi )$. These three alternatives are disjoint. Consequently each logical formula has a unique formula syntax tree and a uniquely determined principal logical connective whenever it is not a logical variable.