Corollary 2
Tag 049S, permanent. Cite it as [Bourbaki, Tag 049S].
Commutative Algebra, chapter II, § 4. Spectra of rings and supports of modules
Let r(a) denote the radical of an ideal a of A; if a and b are two ideals of A, the relation V(a) ⊂ V(b) is equivalent to b ⊂ r(a) and r(b) ⊂ r(a).
It is immediate that the relations b ⊂ r(a) and r(b) ⊂ r(a) are equivalent and, as V(a) = V(r(a)), the corollary follows immediately from Proposition 11, (iii).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.