Corollary
Tag 0B7X, permanent. Cite it as [Bourbaki, Tag 0B7X].
General Topology, chapter I, § 9. Compact spaces and locally compact spaces
For a filter on a compact space to converge it is necessary and sufficient that it has a single cluster point.
Necessity by § 8, no. 1, Proposition 1; sufficiency by Theorem 1 above.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.