Two quotients of projective modules are equal, prove the crossed direct sums of the projective modules and kernels are isomorphic. (Schanuel's Lemma)

Question

We have the following:

$$\alpha_1:P_1\rightarrow M$$

$$\alpha_2:P_2\rightarrow M$$

with $\alpha_1,\alpha_2$ surjective, and $P_1,P_2$ projective. Prove $$P_1\oplus \ker(\alpha_2) \cong P_2\oplus \ker(\alpha_1).$$

I don't know what properties of projective modules I should use.