 Condensed detachment has been used extensively to refine axiomatizations of various implicational logics, especially, in search for shorter and fewer axioms. Some logics may be formulated using axioms (rather than axiom schemas) together with the rule of condensed detachment—without loss of theorems. All the logics that we mentioned so far (\(J_{\rightarrow}\), \(R_{\rightarrow}\), \(T_{\rightarrow}\) and \(E_{\rightarrow}\)) are \(\mathbf{D}\)-complete, that is, they all may be axiomatized by axioms and the rule of condensed detachment. That is, the implicational fragments of classical and intuitionistic logics, and the implicational fragments of the relevance logics \(R\), \(E\) and \(T\) are all \(\mathbf{D}\)-complete.  (See Bimbó (2007) for some further technical details.)