# Axioms of Abelian Category [duplicate]

I know that the one of the axioms of abelian categories is that the induced morphism $\text{coker}(\ker f ) \longrightarrow \ker ( \text{coker} f )$ for any morphism $f$ is an isomorphism. Let's call this axiom $\textit{iso}$.

However, Vakil in his notes (http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf, page 48) mentions axioms (2) and (3). One of my friends remarked that

$$(2) + (3) \Longleftrightarrow \textit{iso} .$$

I have been able to show $\textit{iso} \implies (2) + (3)$ , but how do I show that $(2) + (3) \implies \textit{iso}$?