 Let \(\vdash_C\) be the classical consequence (or derivability) relation and \(\circ (\Gamma)\) express the consistency of the set of formulas \(\Gamma\) such that if \(\circ A\) and \(\circ B\) then \(\circ (A * B)\) where \(*\) is any two place logical connective. Then we can capture derivability in the consistent context in terms of the equivalence: \(\forall \Gamma \forall B\exists \Delta(\Gamma \vdash_C B\) iff \(\circ (\Delta), \Gamma \vdash B)\).