Past exam of the analytic topology and axiomatic set theory course of the University of Oxford / 2009 / B / 6 / iii / a / Solution

Use the bounded formulaIt expresses $x\subseteq y$ with no unbounded quantifier. For parameters $x,y\in U_1$, transitivity puts every member of $x$ in $U_1$ already, and membership in $y$ has the same meaning in both classes. Thus the formula is ${\Delta }_0$ and is absolute in both directions, in particular upward absolute.