Remark

Tag 0A7G, permanent. Cite it as [Bourbaki, Tag 0A7G].

Lie Groups and Lie Algebras, chapter III, § 1. Lie groups

If f is an immersion at e (resp. a submersion at e), clearly f is an immersion (resp. a submersion).

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

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