Proposition 6
Tag 06TW, permanent. Cite it as [Bourbaki, Tag 06TW].
Algebra, chapter V, § 15. Separable extensions
— Every pure extension of a field K is separable. This follows at once from Example 1 (V, p. 119) and Prop. 4 (V, p. 120).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.