I was reading this book by Coorneart Delzant and Papadopoulos. I am stuck with this proposition in Chapter 1(Proposition 1.5)

*If Y is a bounded$\ \delta$-hyperbolic subset of X, then X is$\ \delta'$-hyperbolic with$\ \delta' = \delta + 6 \eta$ where$\ \eta = \sup_{x \in X} dist(x,Y)$*

The authors have not given proof of the proposition. I have tried using the $\ \delta$-hyperbolicity condition of Y but I am getting stuck. Please help.