The zeroth law of thermodynamics provides for the foundation of temperature as an empirical parameter in thermodynamic systems and establishes the transitive relation between the temperatures of multiple bodies in thermal equilibrium.
The law may be stated in the following form:
If two systems are both in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
In mathematics, if A=B and B=C, then A=C. This is called the Transitive Property of Numbers.
In Thermodynamics, the same is true for any two systems. If System A and System B have the same temperature, and System B and System C have the same temperature, then by definition A and C must have the same temperature.
At first glance this may appear obvious, and it is, but its effects on thermodynamics are profound. Multiple such bodies will also transfer heat between each other until they are all at an equilibrium. Ultimately, the lowest energy state possible is called the ground state.