Full Idea
Suppose that a and b have all of their properties in common. a certainly has the property of-being-identical-with-a. So, by supposition, does b. Then a = b.
Gist of Idea
a and b share all properties; so they share being-identical-with-a; so a = b
Source
Baruch Brody (Identity and Essence [1980], 1.2)
Book Reference
Brody,Baruch: 'Identity and Essence' [Princeton 1980], p.9
A Reaction
Brody defends this argument, and seems to think that it proves the identity of indiscernibles. As far as I can see it totally begs the question, since we can only assume that both have the property of being-identical-with-a if we have assumed a = b.