This zeroeth law is sort of a transitive property of thermal equilibrium. The transitive property of mathematics says that if A = B and B = C, then A = C. The same is true of thermodynamic systems that are in thermal equilibrium.
Zeroeth Law of ThermodynamicsTwo systems in thermal equilibrium with a third system are in thermal equilibrium to each other.
One consequence of the zeroeth law is the idea that measuring temperature has any meaning whatsoever. In order to measure a temperature, thermal equilibrium much be reached between the thermometer as a whole, the mercury inside the thermometer, and the substance being measured. This, in turn, results in being able to accurately tell what the temperature of the substance is.
This law was understood without being explicitly stated through much of the history of thermodynamics study, and it was only realized that it was a law in its own right at the beginning of the 20th century. It was British physicist Ralph H. Fowler who first coined the term "zeroeth law," based on a belief that it was more fundamental even than the other laws.
Laws of Thermodynamics