 The last definition is known as the Leibnizian definition of equality. It asserts that x and y are the same if y has every property that x has. Actually, Leibniz called his definition “the identity of indiscernibles” and gave it in the form of a biconditional: x and y are the same if x and y have exactly the same properties. It is not difficult to show that these two forms of the definition are logically equivalent.