Equality: transitive property

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Is the following relation a valid example for the transitive property of equality? If not, what is/are the name(s) of the property/ies involved?

Given A, B, C, D.

Given A = B, A = C, B = D.

Then C = D.

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You are given that $A=B$, $A=C$ an $B=D$.

From the first two you get that $C=B$, and from that and the third one, that $C=D$.

If you want, you've used the transitive propery of equality twice.