Leibniz's Law

Also known as the Law of the Identity of Indiscernibles, Leibniz's Law spells out the necessary and sufficient conditions of the identity relation.

Basically it holds that for 'identity' to be accurately predicated of any two subjects they must share all the same properties. It can be expressed formally as follows:

For any two things x and y, x is equal to y if and only if, for any given property 'F', x has F if and only if y has F.