If $X$ is empty, the inequality $f(x) I_E(x) \leq f(x)$ holds vacuously for all $x \in X$, so assume that $X$ is nonempty and let $x \in X$. If $x \in X \setminus E$, then $f(x) I_E(x) = f(x) \leq f(x)$ holds trivially. If instead $x \in E$, then $f(x) I_E(x) = 0 \leq f(x)$ holds since $f$ is unsigned. $\square$