# Question about the 0th law of thermodynamics

assume I have 3 systems a,b and c.
the equilibrium between a and c can be described by the equality PcVc = f(A1,...., An)
and the same for b and c - PcVc = g(B1,....,Bk).
why does the equality g(B1,...., Bk) = f(A1,...., An) describes an equilibrium between A and B?
the 0th law states that if A and B are in equilibrium with c **for the same value of the thermodynamics coordinates of C**
then they are in equilibrium with each other, but I can find different pairs of Pc and Vc that will result in the same value of PcVc.

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