 The Subset Collection scheme can be regarded as containing a very weak form of Power Set. It asserts, for each formula \(\phi(x, y, z)\) that for every \(A\) and \(B\), there is a set \(C\) such that for each \(z\) such that \(\forall x \in A\exists y \in B[\phi(x, y, z)\)] there is \(R_z \in C\) such that for every \(x \in A\) there is \(y \in R_z\) such that \(\phi(x, y, z)\) and for every \(y \in R_z\) there is \(x \in A\) such that \(\phi(x, y, z)\) (this is the same restriction as in the Strong Collection axiom; notice that not only are images under the relation constructed, but the images are further collected into a set).