Given a logic-based argumentation framework built over a knowledge base in a logical language and a query in that language, the query is universally accepted if it is entailed from all extensions. As shown in [2, 14], universal acceptance is different from skeptical acceptance as a query may be entailed from different arguments distributed over all extensions but not necessarily skeptical ones. In this paper we provide a dialectical proof theory for universal acceptance in coherent logic-based argumentation frameworks. We prove its finiteness, soundness, completeness, consistency and study its dispute complexity. We give an exact characterization for non-universal acceptance and provide an upper-bound for universal acceptance.