Yoneda extensions compute Ext-groups

Exercise 6.4.9. Assume that \(C^{\heartsuit }\) has enough projectives, meaning that for every object \(M\) there exists an epimorphism \(P \twoheadrightarrow M\) from a projective object \(P\). Show that \(\Ext ^n_C(M,N)\) for \(n \geq 2\) can be described in terms of degree \(n\) Yoneda extensions: exact sequences in \(C^{\heartsuit }\) of the form \[ 0 \to N \to E_n \to E_{n-1} \to \dots \to E_2 \to E_1 \to M \to 0. \] Hint: use Proposition 6.4.14 below.