Definition 3

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

Topological Vector Spaces, chapter IV, § 2. Bidual. Reflexive spaces

— A locally convex space E is said to be reflexive if the canonical mapping $c_E$ from E into $E''$ is a topological vector space isomorphism from E onto the strong dual of $E'_b$ .

In particular, a reflexive space is semi-reflexive, hence Hausdorff.

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

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