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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.

The unique readability theorem asserts uniqueness of the outer formation rule and its immediate components in a logical formula. For the fully parenthesized language with negation and implication, every formula is uniquely a variable, a negation of one formula, or an implication between an ordered pair of formulas. It gives a well-defined syntax tree and licenses recursive definitions and structural induction on formulas.