Corollary 3
Tag 0BEP, permanent. Cite it as [Bourbaki, Tag 0BEP].
General Topology, chapter II, § 3. Complete spaces
Every Cauchy filter, which is coarser than a filter converging to a point , also converges to .
This is a consequence of Corollary 2.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.