Example 3

Tag 04IR, permanent. Cite it as [Bourbaki, Tag 04IR].

Commutative Algebra, chapter III, § 5. Flatness properties of filtered modules

If an A-module M is flat and Hausdorff with the $\mathfrak{g}$ -adic topology it is ideally Hausdorff, for $a \otimes_A M$ is then identified with a submodule of M and the $\mathfrak{g}$ -adic topology on $a \otimes_A M$ is finer than the topology induced on $a \otimes_A M$ by the $\mathfrak{g}$ -adic topology on M, which is Hausdorff by hypothesis.

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

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