Restriction_of_Injection_is_Injection

Let $f: S \to T$ be an injection. Let $X \subseteq S$ be a subset of $S$. Let $f \sqbrk X$ denote the image of $X$ under $f$. Let $Y \subseteq T$ be a subset of $T$ such that $f \sqbrk X \subseteq Y$. The restriction $f \restriction_{X \times Y}$ of $f$ to $X \times Y$ is an injection from $X$ to $Y$.