Remark 2
Tag 0AEQ, permanent. Cite it as [Bourbaki, Tag 0AEQ].
Lie Groups and Lie Algebras, chapter III, § 6. Real and complex Lie groups
Let G be a finite-dimensional Lie group. Let H be a subgroup of G. We shall say, by an abuse of language, that H is an integral subgroup of G if there exists a Lie group structure S on H such that H, together with S, is an integral subgroup of G. By Corollary 3 to Proposition 3, if S exists, S is unique.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.