I'm proving equivalent statements for normal, and I'm stuck at this one. Any help getting started would be appreciated.

We are given that (X,\Omega) is a T_1 space and that:

If H and K are disjoint members of \kappa (\Omega), then there exist U \in \Omega such that H\subseteq U and \bar{U}\cap K = \emptyset.

I need to prove that:

Each pair of disjoint members of \kappa (\Omega) have disjoint neighborhoods.