As in Explicit construction of a initial object in a topos I'm looking an elementary proof of the fact that, in a topos, epimorphisms are stable under pullback or, equivalently, that images are stable under pullback. Stardard proofs uses the fact that the pullback functor has right adjoint, hence it preserve colimit.
Proofs can assume the existence of initial object and the image of a morphisms. In particular I'm looking for a proof wich make uses of the internal logic as here: http://ncatlab.org/nlab/show/Trimble+on+ETCS+III