If two system A and B separated by an adiabatic wall. They are separated from system C by a diathermic wall. The system A and C, B and C will reach thermal equilibrium separately. If adiabatic wall between A and B is removed, there will be no exchange of heat showing that A and B are already in thermal equilibrium.
Zero law of thermodynamic implies that temperature is a physical quantities which has the same value for all system which are in thermal equilibrium with each other.
