$Vld\left(\frac{X = X \cap Y}{X \subseteq Y}\right) true \ or false$

Question

$$Vld\left(\frac{X = X \cap Y}{X \subseteq Y}\right) true \ or false$$

My answer: True $$ \forall x((x \in X) \land (x \in Y) \Rightarrow (x \in Y) $$

Feel free to critique my answer and/or add your own using a new method.

Answer 1

Better than what? What if it is not a one liner?

Premise: X = X $\cap$ Y. Conclusion: X $\subseteq$ Y.
Proof. Assume x in X. So x in X $\cap$ Y. Thus x in Y.
Thus for all x in X, x in Y, i.e. X $\subseteq$ Y.