Hom animae in opposite categories

Exercise 1.5.2. Let \(x\) and \(y\) be objects of an \(\infty \)-category \(C\). Show that there is an equivalence \[ \Hom _{C\catop }(x,y) \simeq \Hom _C(y,x). \] Hint: apply \((-)\catop \) to the pullback square defining \(\Hom _C(y,x)\) and use that \(\Hom _C(y,x)\) is an anima.