 Since each of φ1 and φ2 fixes an n-ary truth-function of the variables involved, and these truth-functions are distinct (since φ1 and φ2 were to be non-equivalent) the above Vf / Vg application of Rautenberg’s result tells us that neither of ⊢1, ⊢2, is included in the other. Concentrating on the connectives involved, we can put this by saying that in classical logic any two non-equivalent connectives are incomparable with respect to the subconnective relation (understood as relating the consequence relations on languages in which no further connectives appear). We close by observing that the analogous claim would be false for intuitionistic logic. A counterexample is provided by the connectives defined by φ #1 ψ = ¬φ∨ ¬ψ and φ #2 ψ = ¬(φ ∧ ψ). These are intuitionistically non-equivalent, in the sense of not always yielding ⊢I L-equivalent compounds from the same components, while—by an argument not given here—for any intuitionistically provable sequent σ(#1) involving formulas constructed from the variables by means of #1, the corresponding sequent σ(#2) is also intuitionistically provable (though not conversely). So, by contrast with what can happen in the classical setting, we have non-equivalent connectives one of which is a proper subconnective of the other—understanding this last phrase subject to the same parenthetical qualification as above.