||f(x, x) must be false.
||f(x, y) implies !f(y, x)
||f(x, y) and f(y, z) imply f(x, z).
|Transitivity of equivalence
||Equivalence (as defined above) is transitive: if x is equivalent to y and y is equivalent to z, then x is equivalent to z. (This implies that equivalence does in fact satisfy the mathematical definition of an equivalence relation.)