Amplitude control circuit problem
If \$V_i = 0\$ and the opamp is ideal, then there is no reason for the current through \$R_2\$, \$R_3\$, \$R_4\$ and \$R_5\$ to be identical. Due to negative feedback, the voltage over \$R_1\$ will be 0, and there will therefore be no current flowing through \$R_f\$. The output will be fixed to 0V by the opamp regardless of the resistor values.

Maybe the solution you found is meant for a different circuit, maybe it is not used in the context of superposition, maybe the situation they are trying to describe is something else entirely, or it could also be just wrong. I can only say that the expression you gave does not give you the output voltage for \$V_i = 0\$ as you would do with superposition.