That identity is not a relation between objects is obvious. This becomes very clear if, for example, one considers the proposition “(x) : fx . ⊃ . x = a”. What this proposition says is simply that only a satisfies the function f, and not that only such things satisfy the function f which have a certain relation to a. One could of course say that in fact only a has this relation to a but in order to express this we should need the sign of identity itself.