$(\alpha, \beta)^n=(\alpha^n, \beta^n)$ in Dedekind domains

Question

It is a sometimes useful lemma that if $\mathfrak{a}=(\alpha, \beta)$ is an ideal of a Dedekind domain $A$, then $\mathfrak{a}^n=(\alpha^n, \beta^n)$. Of course, this is easy to prove, but I'd like to be able to just give a reference. However, having looked in Neukirch's, Marcus' and Lang's books, I was not able to find one - do you know a reference for this fact?