 Power-set equality is not upward absolute

Assume $V\ne L$. At the first cumulative stage containing a nonconstructible set, the index is a successor $\beta +1$. Rank absoluteness gives $y=V_{\beta }=(V_{\beta }{)}^L\in L$, not just $V_{\beta }\subseteq L$. Let $x$ be the power set of $y$ computed in $L$. It omits a nonconstructible subset of $y$ from the next external rank stage. Thus $L$ satisfies power-set equality for the parameters $x,y\in L$, while $V$ does not. Both are transitive models of ZF. Subset inclusion itself is bounded and absolute; quantification over all possible subsets causes the failure.