Proof of a relation between phasors of certain harmonic components of memoryless amplifier output signal

It is shown that there holds a relation between the phasors of fundamental components, in the input and output signals, and the phasors of the third order intermodulation (IMD3) components of the output signal, when a sum of a two-tone signal and a signal consisting of components at difference mixing frequencies is sent through a nonlinear memoryless amplifier. This relation can result in an interesting effect. In the output signal, simultaneously the IMD3 products are cancelled and the ratio of the phasors of fundamental components is restored.