Remark 5

Tag 02RL, permanent. Cite it as [Bourbaki, Tag 02RL].

Théories spectrales, chapter III, § 3. Endomorphismes de Fredholm et endomorphismes de Riesz

Let E, F be separated locally convex spaces and $u: E\rightarrow F$ a Fredholm mapping. If $u$ is bijective, then $u$ is an isomorphism (in fact, $u$ is a strict morphism by Prop. 2, (ii)).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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