Lemma 29.57.5. A base change of a morphism with universally bounded fibres is a morphism with universally bounded fibres. More precisely, if $n$ bounds the degrees of the fibres of $f : X \to Y$ and $Y' \to Y$ is any morphism, then the degrees of the fibres of the base change $f' : Y' \times _ Y X \to Y'$ is also bounded by $n$.

**Proof.**
This is clear from the result of Lemma 29.57.2.
$\square$

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