Corollary 1
Tag 07LA, permanent. Cite it as [Bourbaki, Tag 07LA].
Topological Vector Spaces, chapter III, § 1. Bornology in a topological vector space
— Let E and F be two locally convex spaces, and u : E \to F be a continuous linear mapping. If A is a bounded subset of E, then u(A) is bounded in F.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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