Remark 1

Tag 06L0, permanent. Cite it as [Bourbaki, Tag 06L0].

Algebra, V, p. 45, § 7. Separable algebraic extensions

Let E and E' be two separable closures of K. If K is not separably closed, there exist several K-isomorphisms of E onto E'. \* For E is then a non-trivial Galois extension of K, and so there exist K-automorphisms of E distinct from the identity (V, p. 56, Th. 1).

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

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