Let
$X,Y$ sets,
$X_1\subseteq X$,
$Y_1\subseteq Y$,
$F=\mathcal{P}(X\times Y)$ the set of all functions in $X\times Y$,
$F_1=\{f\in F\ |\ \forall x_0((x_0\in\text{dom}(f))\land (x_0\in X_1))\colon f(x_0)\in Y_1\}$.
$(\exists f\in F)\land(\exists x_0(x_0\in\text{dom}(f))\land(f(x_0)\notin Y_1))\implies f\notin F_1$.
