The argument here (identity precludes change) first showed up in Parmenides ca 500 BC. From the Dictionary of Greek and Roman Biography and Mythology:
On the former path [i.e. of reason] we convince ourselves that the existent neither has come into being, nor is perishable, and is entirely of one sort, without change and limit, neither past nor future, entirely included in the present. For it is as impossible that it can become and grow out of the existent, as that it could do so out of the non-existent; since the latter, non-existence, is absolutely inconceivable, and the former cannot precede itself; and every coming into existence presupposes a non-existence.
His writings give us the first example of an explicit premise-and-conclusion argument. Much of Aristotle's metaphysics amounts to an explanation of what's wrong with that argument.