(Assume there exists a in the empty set, now a false proposition implies anything
so this assumption implies that a is in B, so for all a in the null set a is in B)
Also A is not a subset of B if there exists an element a of A which is not in B.
Now this is always true of the empty set as there are no elements of A which are not in B.
So the empty set is a subset of every set.