This paper presents a formalization of an \(\aleph_ 0\)-valued propositional calculus with a single designated value for propositional variables and variable functors which take values from the set \(\{C,C'\}\), where C is Łukasiewicz's implication functor and \(C'PQ =_ T CQP.\) Extending results from the \(\aleph_ 0\)-valued calculus with C as the only primitive functor, the system is shown to be complete, in that all generalized tautologies are theorems.