Full Idea
It is clear from (x)□(x=x) and Leibniz's Law that identity is an 'internal' relation: (x)(y)(x=y ⊃ □x=y). What pairs (w,y) could be counterexamples? Not pairs of distinct objects, …nor an object and itself.
Gist of Idea
With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation
Source
Saul A. Kripke (Naming and Necessity preface [1980], p.03)
Book Reference
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.3
A Reaction
I take 'internal' to mean that the necessity of identity is intrinsic to the item(s), and not imposed by some other force.