''Analytic implications'' in the style of Parry are marked by the property that an implication \(A\to B\) is not considered as true unless the ''content'' of B is already included in that of A. A formal system motivated along these lines was studied, in both an axiomatic and a model-theoretic manner, by \textit{J. M. Dunn} [Notre Dame J. Formal Logic 13, 195-205 (1972; Zbl 0197.275)]. In the present paper the author isolates a subsystem of that of Dunn, which lacks the principle of modus ponens, thus bringing it closer to the usual entailment systems such as E, and proves soundness and completeness with respect to a suitable class of relational models. An interesting feature of these relational models is that instead of two truth-values they use three, identified with the three non-empty subsets of the set of the classical two.