 The Strong Collection axiom scheme asserts that if for every \(x \in A\) there is \(y\) such that \(\phi (x, y)\), then there is a set \(B\) such that for every \(x \in A\) there is \(y \in B\) such that \(\phi(x, y)\) (as in the usual scheme) but also for every \(y \in B\) there is \(x \in A\) such that \(\phi(x, y)\) (\(B\) doesn’t contain any redundant elements). The additional restriction is useful because of the weaker form of the Separation Axiom.