Do the 0th, 1st and 2nd Laws just define temperature, internal energy and entropy?

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swampwiz
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Is the purpose of the 0th, 1st & 2nd Laws of Thermodynamics simply to legitimate the thermodynamic properties of Temperature, Internal Energy & Entropy, respectively?

It seems that all these laws really do is establish that these properties are valid thermodynamic state properties and the underlying transitivity (0th), formula (1st) & constraint (2nd) that are fundamental axioms from which the science of thermodynamics can be constructed.
 
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