The main concept used is the electric field $\mathrm{E}=\frac{\mathrm{dV}}{\mathrm{dr}}$ that suggest the electric potential decreases along the direction of electric field.
Consider a charged conductor and an insulated uncharged conductor.
Now take any path from the charged conductor to the uncharged conductor along the direction of electric field. So, the electric potential decrease along this path from a charge conductor body to infinity.
Now, another path from the uncharged conductor to infinity will again continually lower the potential further. This ensures that the uncharged body must be intermediate in potential between that of the charged body and that of infinity.