I'm not convinced that it is right.

Vx occurs at the airspeed where excess thrust is maximized, while Vy
occurs at the airspeed where excess power is maximized. Off the top of my
head, I don't see any reason to believe that for a jet, that it's a given
that maximum excess thrust would occur at a constant airspeed with respect
to altitude.

The ***TAS*** would definitely increase, but the drag/thrust curve moves to
the right rather than to the right and up like the power required curve. As
far as I can tell, and I'm basing it (probably WAY too much) on the
interactive program found at this page
http://www.professionalpilot.ca/aero.../climb_jet.htm, the
***IAS*** remains almost constant for a jet.

Confusing stuff.