Proposition 3
Tag 0A1U, permanent. Cite it as [Bourbaki, Tag 0A1U].
Lie Groups and Lie Algebras, chapter II, § 1. Enveloping bigebra of a Lie algebra
If the cogebras is coassociative (resp. cocommutative) (Algebra, Chapter III, § 11, no. 2), so is the cogebras .
This follows from the following lemma:
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.