The Stacks project

Proof. Let $\{ T_ i \to T\} $ be an fppf covering of schemes, see Topologies, Definition 34.7.1. Observe that $T_ i \to T$ is locally of finite type. Let $U \subset T$ be an affine open. It suffices to show that $\{ T_ i \times _ T U \to U\} $ can be refined by a standard ph covering, see Topologies, Definition 34.8.4. This follows immediately from Lemma 37.48.6 and the fact that a finite morphism is proper (Morphisms, Lemma 29.44.11). $\square$