The QBF validity problem with any propositional formulamay be seen as a QCSP. In this frame, we introduce a new constraint: the equivalence constraint and prove that it is stronger than equality constraint. In order to design this equivalence constraint, we introduce a new sequent calculus for QBF which is based on an equivalence relation over subformulae. This sequent calculus is proven to be sound and complete w.r.t. the semantics of the QBF. Based on this system, we define our equivalence constraint in such a way that QCSP(QBF) may be seen as a CSP(QBF) with a quantied search algorithm. We report some experiments in a generic constraint development environment.