A surprising result of Pitts (1992) says that propositional quantifiers are definable internally in intuitionistic propositional logic (IPC). The main contribution of this paper is to provide a formalization of Pitts’ result in the Coq proof assistant, and thus a verified implementation of Pitts’ construction. We in addition provide an OCaml program, extracted from the Coq formalization, which computes propositional formulas that realize intuitionistic versions of $\exists p \phi$ and $\forall p \phi$ from $p$ and $\phi$.