 The problem of finding a canonical axiomatization for non-finitely axiomatizable products of finitely axiomatizable logics was solved in Hampson, Kikot, Kurucz and Marcelino 2020, by analyzing two-dimensional modal product logics involving the unimodal logic of the difference Diff, introduced by von Wright 1979 as the logic of ‘elsewhere’. This logic is defined by the set of unimodal formulas that are valid in all the frames \(\langle W,\neq_{W}\rangle\), where \(\neq_{W}\) is the non-identity relation on a non-empty set \(W\); these frames are called difference frames. The logic Diff can be characterized as the logic of all the frames \(\langle W,R\rangle\) where \(R\) is a pseudo-equivalence relation, that is, where \(R\) is symmetric and pseudo-transitive: if \(R(x,y)\) and \(R(y,z)\) then either \(x=z\) or \(R(x,z)\).  Since, in particular, equivalence relations are frames for Diff, the latter is a sublogic of S5.  The paper proves that, despite Diff is a finitely axiomatizable subsystem of S5, the two-dimensional product logic Diff\(\,\times\,\)Diff is non-finitely axiomatizable, and can be axiomatized by infinitely many Sahlqvist axioms. Let Diff\(\,\times^{sq}\,\)Diff be the ‘square’ version of Diff\(\,\times\,\)Diff, which is characterized by the family of all the products \(\langle U,\neq_{U}\rangle \times \langle V,\neq_{V}\rangle\) of difference frames such that the sets \(U\) and \(V\) have the same cardinality; hence Diff\(\,\times^{sq}\,\)Diff contains the logic Diff\(\,\times\,\)Diff. The paper proves that the former is not a finite axiomatic extension of latter, and can be axiomatized by adding infinitely many Sahlqvist axioms. The modal logics Diff\(\,\times\,\)Diff and Diff\(\,\times^{sq}\,\)Diff are the first examples of products of finitely axiomatizable modal logics that are not finitely axiomatizable, although axiomatizable by explicit infinite sets of canonical (Sahlqvist) axioms. 