On the abstract of a paper by Emily Riehl and Dominic Verity, it is stated that

Every quasicategory arises as a the homotopy coherent nerve of a simplicial category up to equivalence.

Where can one find a proof of this statement?

On motivation for the question, HTT 4.2.4.1 would then imply that any colimit in a quasicategory could be computed as a homotopy colimit of a diagram $F\colon\mathbf{J}\rightarrow\mathbf{C}$, where $\mathbf{J}$ and $\mathbf{C}$ are simplicial categories.

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