A deduction system, called RE--proof system, is constructed for generatingthe revisions of first order belief sets. When a belief set is rejected by a given fact, allmaximal subsets of the belief set consistent with the fact can be deduced from the proofsystem. The soundness and completeness of the RE--proof system are proved, which imply that there exist a resolution method to decide whether a revision retains a maximal subset of a belief set.