(x)(y)[ (x = y)  ≡  (F)(Fx  ≡  Fy) ]

"... items are numerically identical just in case any property had by either one of them is also had by the other." (IP3 293b)

In other words: A is B if and only if whatever is true of A is true of B and vice versa.

Example: A cloud is a visible mass of water particles suspended in the air if and only if whatever is true of a cloud is true of a visible mass of water particles suspended in the air, and whatever is true of a visible mass of water particles suspended in the air is true of a cloud.