This question is from Set Theory, Jech(2006), Page 70, 6.5.
Rank function is defined as on Page 64:
- $V_0=\emptyset$,
- $V_{\alpha+1}=P(V_{\alpha})$,
- $V_{\alpha}=\bigcup_{\beta<\alpha}V_\beta$, if $\alpha$ is a limit ordinal.
$\mathrm{rank}(x)=\operatorname{min}\{\alpha \in \mathrm{Ord}:x \in V_{\alpha+1}\}$