Proof. You can prove this in many different ways. One way is to use the snake lemma (Lemma 10.4.1), the Jacobi-Zariski sequence (Lemma 10.134.4), combined with the characterization of projective modules as being direct summands of free modules (Lemma 10.77.2). Another proof can be obtained by combining Lemmas 10.137.10, 10.137.9 and 10.137.13. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).