In order to prove that entropy is a property, we will suppose two cycles i.e. 1-A-2-B-1 and 1-A-2-C-1 as shown in

For_1-A-2-B-1:

$\int_{1-A-2} ∂Q / T + \int_{2-B-1} ∂Q / T = 0$

For_1-A-2-C-1:

$\int_{1-A-2} ∂Q / T + \int_{2-C-1} ∂Q / T = 0$

$\int_{2-C-1} ∂Q / T = \int_{2-B-1} ∂Q / T$

Hence, $∫ δQ / T$ are a definite quantity independent of the path followed for the change and depend only upon the initial and the final states of the system.

Hence entropy is a property.