For those with a more graphic mind, just imagine the torque curve of the engine and the torque curve of the propeller. Where they intersect, the system is in stable equilibrum (as the propeller curve will always be steeper than the engine curve above idle). The propeller curve is parabolic, torque increases with speed to the power of 2. Increasing TAS (roughly) shifts the curve to the negative ("downwards"), the new intersection therefore is at higher rpm.