elementary set theory - Proof for Image of Indexed Collection of Sets?

Trying to prove that if f is one-to-one, then

$$f\left(\bigcap\{U_\alpha:\alpha \in \Lambda\}\right)=\bigcap\{f(U_\alpha):\alpha\in\Lambda\}$$

I am able to prove that:

$$f\left(\bigcap\{U_\alpha:\alpha \in \Lambda\}\right)\subseteq\bigcap\{f(U_\alpha):\alpha\in\Lambda\}$$

However, I do not really know where to begin the proof for:

$$\bigcap\{f(U_\alpha):\alpha\in\Lambda\}\subseteq f\left(\bigcap\{U_\alpha:\alpha \in \Lambda\}\right)$$