Corollary

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

Topological Vector Spaces, chapter IV, § 3. Dual of a Fréchet space

— The bidual of a locally convex metrizable space is a Fréchet space.

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

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