The result appears in Diaconescu's thesis (Dalhousie '73) with `Set' generalized to an elementary topos, Proposition I.1.5 .
From the preceding text one gets the impression that the result was already well known for `Set' but none of Diaconescu's references are likely sources.
Diaconescu's proofs of results about "internal category theory" contain truly marvelous diagrams the like of which we will probably not see again until various TeX issues are settled. At the time it seems that rigor demanded them but that was before indexed categories, fibrations and languages were well understood. It is now clear that a careful proof of the result in question, written as for sets, suffices. It would be useful to have the result and similar ones proved in a text or expository paper. I do not know of one. RJ Wood ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++