Remark 3.1.1.9. Let $f: X_{} \rightarrow S_{}$ be a Kan fibration of simplicial sets. Then, for every vertex $s \in S$, the fiber $\{ s\} \times _{ S_{} } X_{}$ is a Kan complex (this follows from Remark 3.1.1.6 and Example 3.1.1.2).
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