From the The Stanford Encyclopedia of Philosophy.:

The Identity of Indiscernibles (hereafter called the Principle) is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

âˆ€F(Fx â†” Fy) â†’ x=y.

Or, in more prosaic terms: If two objects share exactly the same set of properties, then they are the same thing.

But there's a dark side to metaphors. They're never quite exact. If they were they'd be the same thing. In some cases, those differences can lead us astray.

Leibnitzâ€™s principle of the identity of indiscernibles applies to entity types. That means entities P and Q are the same entity type if every attribute possessed by P is also possessed by Q.