Proposition 3

Tag 0BDP, permanent. Cite it as [Bourbaki, Tag 0BDP].

General Topology, chapter II, § 2. Uniformly continuous functions

If $\mathfrak{U}_1$ and $\mathfrak{U}_2$ are two uniformities on a set X, then $\mathfrak{U}_1$ is finer than $\mathfrak{U}_2$ if and only if every entourage of $\mathfrak{U}_2$ is an entourage of $\mathfrak{U}_1$ .

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

Cited by

Corollary, § 2

Cites

Nothing.