Lemma 31.34.2. Let $X$ be a quasi-compact and quasi-separated scheme. Let $U \subset X$ be a quasi-compact open subscheme. Let $b : X' \to X$ be a $U$-admissible blowup. Let $X'' \to X'$ be a $U$-admissible blowup. Then the composition $X'' \to X$ is a $U$-admissible blowup.

** Admissible blowups are stable under composition. **

**Proof.**
Immediate from the more precise Lemma 31.32.14.
$\square$

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Comment #833 by Johan Commelin on