The notion of identity under consideration here is that of numerical identity as opposed to qualitative identity .
Every object is numerically identical to itself and to no other thing.
The desk I write at, for example, is numerically identical to itself only, though there are, no doubt, many other desks which are exactly similar and so are qualitatively identical to it. Where x and y are objects and f is a property or relation. Consider a person, Harry, who is tanned in the summer and who has lost his tan and so is not tanned in the winter. But, this appears to be a direct violation of Leibniz Law. If the person in the summer and the person in the winter really are identical, then they should, according to Leibniz Law, share all of their properties.