Enderton defines the rank of a set $A$ to be the least ordinal $\alpha$ such that $A \subseteq V_{\alpha}$ (equivalently, $A \in V_{\alpha^+}$). He the derives the following identity: $rank(A) = \bigcup \{ (rank(x))^+ : x \in A \}$ for all sets $A$.
In Exercise 30 of Chapter 7, the reader is asked to prove several identities involving rank. For instance, that $rank\{a,b\} = max(rank(a),rank(b))^+$. I am having trouble proving the second identity, that $rank(\wp(x)) = rank(x)^+$ for all sets $x$. I am not sure whether I am missing some elementary identity that would let me prove the identity, or whether I am misunderstanding the definition of rank.
Clearly, $z \in rank(\wp(x)) \Leftrightarrow (\exists y)(y \subseteq x \wedge (z \in rank(y) \vee z = rank(y))$. On the other hand $z \in (rank(x))^+ \Leftrightarrow (\exists y)(y \in x \wedge z \in (rank(y))^+) \vee z = rank(x)$. I'm not sure why the first statement should imply the second, and conversely, however.