Example 1

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

Topological Vector Spaces, chapter II, § 1. Semi-norms

A norm on E is a semi-norm $p$ such that the relation $p(x) = 0$ implies that $x = 0$ (I, p. 3).

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

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