Reference to the Inverse Mapping Theorem involving Banach spaces

Question

I would like a reference that has the proof of the following theorem:

Inverse Mapping Theorem: Let $X,Y$ be two Banach spaces, $\Omega \subseteq X$ an open subset and $a\in \Omega$. Suppose that $f:\Omega \to Y$ is a map of class $C^k$ with $k\in \mathbb{N}^\times \cup\{\infty\}$. If the differential $(df)_a\in \mathcal{L}(X,Y)$ is invertible, then there's a open neighborhood $U\subseteq \Omega $ of $a$ such that $f[U]\subseteq Y$ is open and $U\to f[U], x\mapsto f(x)$ is a $C^k$-diffeomorphism.

Thank you for your attention!

Answer 1

Jean Dieudonne, Treatise On Analysis Volume I, page 273.