J-K flip-flops are the most general elementary units in sequential digital circuits. By extending Boolean operations to their respective fuzzy counterparts various fuzzy flipflops (F3) can be defined. Because of the axiomatic properties of fuzzy operations are considerably weaker then the properties satisfied by Boolean lattices, the minterm and maxterm type definitions of the same F3 are as a rule not equivalent. In former work we found a unique exception where simulation investigations lead to identical results for all parameter combinations examined. The base of this unique F3 is a pair of non-associative fuzzy connectives. In this paper the exact proof is given for the identity of the two definitions, i.e., for the uniqueness of the definition of this special non-associative F³.