Corollary

Tag 07ME, permanent. Cite it as [Bourbaki, Tag 07ME].

Topological Vector Spaces, III, p. 13, § 2. Bornological spaces

— Every Fréchet space (II, p. 24) is the inductive limit of Banach spaces.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Nothing.