 Here we point out that many-sorted reduces to classical first-order logic (one-sorted) in the following sense: given a many-sorted structure \(\mathcal{A}\), every many-sorted sentence true at \(\mathcal{A}\) has a translation into one-sorted first order logic that is true at \(\mathcal{A}^{\ast}\), where \(\mathcal{A}^{\ast}\) is the result of unifying all the sorts in \(\mathcal{A}\). From this result we obtain the equivalence between consequences in both logics, modulo a theory \(\Pi\) easily defined.