Definition 1
Tag 0082, permanent. Cite it as [Bourbaki, Tag 0082].
Algebra, VIII, p. 120, § 7. Simple Rings
We say that a ring A is simple if it satisfies the equivalent conditions (i), (ii), and (iii) of Proposition 1. Let K be a commutative field; a K-algebra is called simple if its underlying ring is simple.
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.