Question about axiom A4 of abelian category

Question

Let $\mathcal{A}$ be an additive category. If one requires only the existence of kernels and cokernels, then for any morphism $\varphi:X\rightarrow Y$, there exist two diagram \begin{equation} K\overset{k}{\rightarrow}X\overset{i}{\rightarrow}I,\ I'\overset{j}{\rightarrow}Y\overset{c}{\rightarrow}K' \end{equation} with $k=\text{ker}\varphi,i=\text{Coker}k,c=\text{Coker}\varphi,j=\text{ker}c$. Then there is a morphism $l:I\rightarrow I'$ such that $\varphi=j\circ l\circ i$. How to prove $l$ is both a mono and an epi? It's an exercise in Gelfand's book.