How to prove $(A \cap B) \cap C \subseteq A \cap (B \cap C)$

Question

My try:

Suppose $x \in \ (A \cap B) \cap C$. We know $x \in (A \cap B)$ and $x \in C$. We can specialize and say that $x \in A$ and $x \in B$ and $x \in C$.

From there I don't know how to synthetize the other set.

Answer 1

$$(A \cap B) \cap C \subseteq A \cap (B \cap C)$$ $$x\in(A\cap B)\cap C$$ $$(x\in A\mbox{ and }x\in B)\mbox{ and }x\in C$$ $$x\in A\mbox{ and }(x\in B\mbox{ and }x\in C)$$ $$x\in A\cap(B\cap C)$$