A and B are subsets of X

give a formal proof that $\displaystyle (A union B)^1 = A^1 intersect B^1$

I know that $\displaystyle (A union B)^1$ contains the set of elements that are in X that are not in the union of A and B

and i know that $\displaystyle A^1 intersect B^1$ contains the set of elements resulting from the intersection of the elements that are in X and not in A or B

How can i build a formal proof from this?

Thank you in advance