A set is determined and sometimes even defined by all its elements. If you take away all the elements of a set, you take away the set. If it is not true that you take away all the elements of a set, you do not take away the set. Thus by Biconditional Introduction: you take away all the elements of a set if and only if you take away the set. This biconditional suggests a set and all its elements are the same. There is nothing more to a set other than all its elements. The empty set actually and technically is not a set because there are no elements to determine the empty set. The empty set is not a set just as a person who runs 0 feet does not run.