How does one prove that, for an infinite set A, that = , that is, that the set of all functions from A to A has the same cardinality as the set of all functions from A to {0,1}, or equivalently the power set of A?

The moderator asked posters to indicate the proof system in which one is working. The usual set-theoretical methods are fine. I am not working in the constructive universe. If singular cardinals give problems, assume that |A| is a regular cardinal.