If we apply this construction to the family \(A_n = \E_{m,2n}\) we see that \((\Sigma n \in {{\mathbb N}})\E_{m,2n}\) is nonempty exactly when there is an \(n\in {{\mathbb N}}\) with \(m=2n\). Using the general set-theoretic product operation \((\Pi n \in {{\mathbb N}})A_n\) we can similarly obtain a set corresponding to a universally quantified proposition.