It is a very simple concept that does not require an indepth discussion.
Climb speeds change with altitude.
It does not matter if we are talking Indicated or True airspeed, they both change.
In fact, Indicated airspeed for Vy decreases with altitude and Indicated airspeed for Vx increases with altitude.
Where they meet is the aircraft's absolute ceiling.
http://aerosrv.cls.calpoly.edu/dbiez...20and%20Vy.pdf