Mapping out of animae into groupoid cores

Exercise 1.4.13. Show that for an anima \(X\) and an \(\infty \)-category \(C\) the core functor \(\gamma _C\colon C^{\simeq } \to C\) induces an equivalence \[ \Map (X,C^{\simeq }) \iso \Map (X,C). \] Hint: Apply the groupoid core axiom to the evaluation functor \(\Map (X,C)\times X\to C\), and then curry and pass to the core once more.