Corollary 2

Tag 0A88, permanent. Cite it as [Bourbaki, Tag 0A88].

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

Suppose that $G_0$ operates trivially on $E_0$ . Let $E'$ be the trivial $G$ -bundle with base space $X$ and fibre $E_0$ . There exists one and only one isomorphism of $E$ onto $E'$ compatible with the operations of $G$ and extending $\mathrm{Id}_{E_0}$ .

This follows immediately from Proposition 17.

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

Cited by

Proposition 6, § 2

Cites

Proposition 17