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Proof. This is true because a Zariski covering of an affine scheme can be refined by a standard ph covering by Lemma 34.8.3. $\square$

[1] We will see in More on Morphisms, Lemma 37.44.7 that fppf coverings (and hence syntomic, smooth, or ├ętale coverings) are ph coverings as well.

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