Lemma 29.37.6. Let $f : X \to S$ be a morphism of schemes. Then $f$ is quasi-affine if and only if $\mathcal{O}_ X$ is $f$-relatively ample.

[II Proposition 5.1.6, EGA]

**Proof.**
Follows from Properties, Lemma 28.27.1 and the definitions.
$\square$

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