Remark 1
Tag 078A, permanent. Cite it as [Bourbaki, Tag 078A].
Topological Vector Spaces, chapter I, § 1. Topological vector spaces
In a normed space on a non-discrete valued division ring the set of open balls (resp. closed balls) with centre 0 is a fundamental system of neighbourhoods of 0 which satisfy the conditions (EV_I), (EV_II) and (EV_III).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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