 The voltage measurement should ideally not involve a flow of current through the meter, so "I"2 = "I"3 = 0.It follows that
In other words, the chemical potentials "µ2" and "µ3" and their respective voltages and are the same.As a consequence of no drop of voltage between the contacts 2 and 3, the current "I"1 experiences zero resistivity "R"SdH in between contacts 2 and 3
The result of zero resistivity between the contacts 2 and 3 is a consequence of the electrons being mobile only in the edge channels of the sample.