# The cokernel of an irreducible monomorphism is always the third term of an AR sequence with indecomposable middle term?

I recently studied the structure of the AR quiver of Dynkin type $\mathbb{A}_n/I$, $\mathbb{D}_n/I$ with $I$ any admissable ideal, and found that the cokernel of an irreducible monomorphism is always the third term of an AR sequence with indecomposable middle term, and dually the kernel of an irreducible epimorphism is always the first term of an AR sequence with indecomposable middle term. But I hardly find any idea to prove it. Any suggestions are welcome!

Here irreducible means irreducible morphisms between indecomposable modules.