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