Lemma 35.28.1. The property $\mathcal{P}(f)=$“$f$ is locally of finite presentation” is fppf local on the source.

**Proof.**
Being locally of finite presentation is Zariski local on the source and the target, see Morphisms, Lemma 29.21.2. It is a property which is preserved under composition, see Morphisms, Lemma 29.21.3. This proves (1), (2) and (3) of Lemma 35.26.4. The final condition (4) is Lemma 35.14.1. Hence we win.
$\square$

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