If $X = \emptyset$, then the claim follows from R125: Subset relation is reflexive.

Consider then the case $X \neq \emptyset$. For $\emptyset$ not to be a subset of $X$ would require the existence of an element of $\emptyset$ that does not belong to $X$. If such an element were to exist, that would imply that $\emptyset$ is not empty, which is a contradiction. Hence, such element does not exist and therefore $\emptyset$ is a subset of $X$.