Does the simplicial-set internal hom of quasicategories give a quasicategory?

Question

The internal hom structure on simplicial sets is described here. This provides us with a functor $h : C^{\text{op}} \times C \rightarrow C$ where $C := \mathrm{Sets}^{\mathbf{\Delta}^{\text{op}}}$.

My question is, if some given $X,Y \in \mathrm{Obj}(C)$ are in fact quasicategories, then is $h(X,Y) \in \mathrm{Obj}(C)$ also a quasicategory? Would anyone know of a reference that discusses this?

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Update: I have found a discussion of this in Lurie's Higher Topos Theory, Proposition 1.2.7.3, and the Proposition following 2.2.5.7.

Answer 1

Reference: see Lurie, Higher Topos Theory, Proposition 1.2.7.3.

Also see the Proposition following 2.2.5.7; it is a proof of 1.2.7.3.