That's the deMorgan law proof for sets or whatever.

You take the left side or the right side, write out what it means to be a union and stuff just a base definition.

So say the left side:

Let's let

So combine it: (I don't really remember what I did when I did this the first time but it gets kinda messy)

Then you do the same to the right side and you can see they're equal.