 A consequence of the axiom of replacement in constructive Zermelo–Fraenkel set theory,  CZF,  is that if \(A\) is a set and \(B\) is a class that is equinumerous with \(A\), then \(B\) is also a set. It follows that the class  \[ \textrm{dch}(\bN)≡ \{S \subset\bN : \forall x \in \bN (x \in S \vee x \not\in S)\} \]  of detachable subsets of \(\bN\), being equivalent to \(2^{\bN}\), is a set. 