Let $j:W\to X$ be a closed immersion of a schemes and $f:Y\to X$ a morphism. The basechange of $j$ along $f$ defines a closed immersion $W\times_X Y\to Y$.
The inclusion $k:X\setminus W\to X$ and the inclusion $l:Y\setminus (W\times_X Y)\to Y$ are both open immersions.
Is the fiber product $$ (X\setminus W)\times_X Y $$ isomorphic to $Y\setminus(W\times_X Y)$ in the canonical way, i.e. is $l$ the basechange of $k$ along $f$?