 The hybrid of two connectives is a subconnective of each of them in the sense that whatever sequents (of the logical framework in play) are provable for it are provable for them. And conversely—but for the moment the subconnective relation itself will be the focus of attention. Intuitionistic negation is in this sense a subconnective, indeed a proper subconnective (in the sense that we do not have the converse) of classical negation. As with hybrids, there are various options, of differing degrees of generality in their application, for defining this relation. In the case of a language with only a single primitive connective, #, we can say that # as it behaves according to (e.g.) the consequence relation ⊢ is a subconnective of # as it behaves according to ⊢′ just in case ⊢ ⊆ ⊢′. If we want to allow different connectives of the same arity, say # and #′, then we can put this instead by saying that σ(#) ∈ ⊢ only if σ(#′) ∈ ⊢′, for all σ(#), understanding the latter to denote a sequent with various occurrences of # in its constituent formulas, with σ(#′) the result of replacing all such occurrences by #′. This kind of formulation lends itself to wider applicability since we can allow other connectives in the formulas of σ(#), provided these are in the language of ⊢′. There is no reason to restrict attention to primitive connectives in making such comparisons. For example, each of ☐ and ☐☐ is a subconnective of the other in several well-known modal logics, as is shown in Zolin (2000), where logics are developed axiomatically as sets of formulas (sequents of the logical framework Fmla, as we would  say[12])  so the “σ(#)” would become “φ(#)” and the point is that in the logics concerned φ(☐) and φ(☐☐) are always equi-provable—though in the interesting cases (e.g., those of K, KT, KTB), not provably equivalent. Note that this is an intra-logical application of the subconnective idea (corresponding to the case of ⊢ = ⊢′ above, for which we definitely need to work with notationally distinguished # and #′). Zolin calls such mutual subconnectives analogous (‘analogous modalities’). A philosophically famous example of this phenomenon from bimodal (or more specifically, doxastic-epistemic) logic was reported in Byrd (1973).