M. Eidelheit [Stud. Math. 6, 139–148 (1936; Zbl 0015.35603)] showed that every non-normable Fréchet space \(E\) has a quotient isomorphic to \(\omega\), the space of all sequences. P. Perez Carreras and J. Bonet [Collect. Math. 33, 195–200 (1982; Zbl 0529.46001)] showed that finite-codimensional subspaces of \(E\) have quotients isomorphic to \(\omega\), too. In this article, the author proves the same statement for countable-codimensional subspaces of non-normable Fréchet space \(E\). For the proof, he uses the other theorem mentioned in the title: every countable-codimensional subspace of any infinite-dimensional Fréchet space \(E\) has an infinite-dimensional Fréchet quotient.