Prove that $A\subseteq B\Longleftrightarrow A\cap B = A$ In set theory logic mathematics. How would i do the proof for: $A\subseteq B\Longleftrightarrow A\cap B = A$

If $A \subseteq B$, then the $\Rightarrow$ part is true, since all elements of $A$ are also elements of $B$ - proceed next by using the definition of $\cap$. If $A\cap B=A$, then all the elements of $A$ are also elements of $B$, by definition of $\cap$. Thus, $A\cap B=A\implies A\subseteq B$, i.e., $A\subseteq B\iff A\cap B=A$.
