Corollary 2
Tag 0AJ7, permanent. Cite it as [Bourbaki, Tag 0AJ7].
Lie Groups and Lie Algebras, chapter III, § 9. Commutators, centralizers and normalizers in a Lie group
Every analytic subgroup of consisting of unipotent elements is a simply connected Lie subgroup.
This follows from Propositions 13 (ii) and 18 (ii) and the fact that the lower strict triangular group is simply connected.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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