 Note that \(\phi\) here does not need to be functional; if for every \(x \in A\), there are some \(y\)s such that \(\phi(x, y)\), there is a set such that for every \(x \in A\), there is \(y\) in that set such that \(\phi(x, y)\). One way to build this set is to take, for each \(x \in A\), all the \(y\)s of minimal rank such that \(\phi(x, y)\) and put them in \(C\). In the presence of all other axioms of ZFC, Replacement and Collection are equivalent; when the axiomatics is perturbed (or when the logic is perturbed, as in intuitionistic set theory) the difference becomes important. The Axiom of Foundation is equivalent to \(\in\)-Induction here but not in other contexts: \(\in\)-Induction is the assertion that for any formula \(\phi\):