 Earlier in this section we saw that, where Vf and Vg are the classes of valuations for a language with n-ary connective # on which distinct truth-functions f and g are associated with # respectively, the consequence relations determined by Vf and Vg were always distinct. In the present terminology, this means that either # as it behaves according to the first of these consequence relations is not a subconnective of # as it behaves according to the second, or vice versa. This is obvious for generalized consequence relations as one can read off the difference from the unconditional conditions induced by the determinants of f and g, but we saw (in a worked example) that such differences are also guaranteed to emerge at the relatively cruder level of consequence relations. A stronger conclusion can be drawn from Theorem 4 of Rautenberg (1981) (see also Rautenberg 1985, p. 4), which will not be proved here, and for the statement of which we need to explain that a non-trivial consequence relation ⊢ is one for which there exist formulas φ, ψ in the language of ⊢ such that φ ⊬ ψ; for some of the matrix terminology here, see Section  5: