Corollary 3
Tag 07O9, permanent. Cite it as [Bourbaki, Tag 07O9].
Topological Vector Spaces, chapter III, § 4. The Banach-Steinhaus theorem
— Every inductive limit of barrelled spaces is a barrelled space.
We shall prove later (IV, p. 14, corollary) that every product of barrelled spaces is barrelled.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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Nothing.