Consistency is one of the most fundamental syntactic concepts in mathematical logic. By treating consistency in an abstract way, Smullyan presented abstract consistency class, and proved the socalled Smullyan's unifying principle. In this paper, considering various properties possessed by the class of consistent sets of wffs in first-order logic system, we generalize the concept of abstract consistency class into the most general form-universal abstract consistency class, and further prove its universal unifying principle. This result can be used to prove the completeness theorems of first-order logic system and the universal refutation method proposed by us.