An extension, QLP, of the propositional logic of explicit proofs, LP, is created, allowing quantification over proofs. The resulting logic is given an axiomatization, a Kripke-style semantics , and soundness and completeness are shown. It is shown that S4 embeds into the logic, when we translate the necessity operator using a quantifier: there exists an explicit proof. And it is shown that the propositional part of QLP is exactly LP. No connection with arithmetic provability is made.