As you say, we need to prove that each set is a subset of the other, in order to prove they're equal. So let's prove first that . We do this by choosing an element in the first set, and showing that it's also in the second.
So let's suppose that . That means that there's an for which .
So we've just proved that . In other words, that
OK? Now you've got to prove it the other way round. Start with and ...