I have been asigned this problem in class.

$\displaystyle C\subseteq A \Rightarrow (A \cup B) \cap C \subseteq A $

Can you aid me in how should i start. I thought of puting it in terms of propositional logic, then proving it. The propositional logic equivalent I came up with

$\displaystyle (C \Rightarrow A) \Rightarrow (A \vee B) \wedge (C \Rightarrow A )$

Is this correct?