Proof of the associated Lie algebra is isomorphic to $T_e(G)$

Question

I´m looking for a book with the proof of the result that says the associated Lie algebra of a Lie group $G$, let be $G_{Lie}$, is isomorphic to the tangent space $T_e(G)$, where $e \in G$ is the neutral element.

Let me said the chapter or theorem, not only the book, please.

Thank you all

Answer 1

Look at Introduction to Smooth Manifolds, 2nd edition by John Lee (great book). This is theorem 8.37, page 191.