Corollary
Tag 0A26, permanent. Cite it as [Bourbaki, Tag 0A26].
Lie Groups and Lie Algebras, chapter II, § 1. Enveloping bigebra of a Lie algebra
Let gi (i = 1, 2) be a Lie algebra, U(g_i) its enveloping bigebra and σ_i : g_i → U(g_i) the canonical mapping. For every Lie algebra homomorphism h : g_1 → g_2, the unital algebra homomorphism U(h) : U(g_1) → U(g_2) such that U(h) ∘ σ_1 = σ_2 ∘ h (Chapter I, § 2, no. 1) is a bigebra morphism.*
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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