"Two sets are equal if and only if for any element of A if and only if is an element of B".
Since A has no elements the statement,
"If x in A then x in B" is true.
"If x in B then x in A" is true.
These statements are true because the hypothesis of the conditional is false. And a false impling a true of a false impling a true is always true. Thus these statements are both true.