The Law of Identity (ID)

Each thing, whether a universal or a particular thing, is composed of its own, unique, set of characteristic qualities/properties, which in ancient Greece was known as its essence.

The law of identity states that each thing is identical with itself, denoted by $\forall x\ . x=x$

The modern formulation of identity is that of Gottfried Leibniz: $x$ is the same as $y$ iff every predicate true of $x$ is true of $y$ as well.