When we have an inverting amplifer circuit using opamps, we have resistor R1 which between the voltage input and the opamp, then we have resistor Rf which is between the input of the opamp and Vo. If we assume that V- of the opamp and V+ of the opamp are both zero, doesn't this mean that we should have a constant I1 current. For example if R1 is 100 ohm and the input voltage is 5V, we should have a constant current of 0.05A I1?
Yes - you are correct.
There is a constant current of I1=Vin/R1=50mA (for R1=100 Ohms and Vin=5V). This current goes through the feedback resistor Rf (because we are allowed to assume that no current enters the high-resistive opamp input).
Therefore Vout=-I1*Rf=-(Vin/R1)*Rf. This gives us the classical gain expression