In the question Do pushouts preserve monic? it is said that monics in a topos are stable under push out. I would like a precise reference or a nice proof of this fact for elementary topoi (for Grothendieck follows since it holds in Sets, then in presheaves and then in sheaves (pointwise computation + associated sheaf).
This is half of Corollary 2.4.3 in [Sketches of an elephant, Part A]. Here is (a paraphrase of) the proof:



Just for reference, this is also the first half of corollary 4, ch. IV10 in MacLaneMoerdijk "Sheaves in geometry and logic". The proof follows the same idea as the proof in Zhen Lin answer, except that the map $h: B \to PC$ is obtained using the previously proved property that $PC$ is injective, so that $\{.\}g$ extends to $B$. 

