proves a more general result, which does not require that \phi(\cdot,z) is differentiable. Instead it assumes that \phi(\cdot,z) is an extended real-valued closed proper convex function for each z in the compact set Z, that \operatorname{int}(\operatorname{dom}(f)), the interior of the effective domain of f, is nonempty, and that \phi is continuous on the set \operatorname{int}(\operatorname{dom}(f)) \times Z. Then for all x in \operatorname{int}(\operatorname{dom}(f)), the subdifferential of f at x is given by
