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I came across a statement that says that in BCNF, a prime attribute cannot be transitively dependent on a key.

But consider a relation R (A, B, C)

    where,   A --> ABC ,   B --> ABC ,  C --> ABC

Clearly it is in BCNF and each of A, B and C are candidate keys.     

Now A --> B and B --> C and A --> C . Thus, we can tell C(a prime attribute) is transitively dependent on A (a candidate key) !!

Where am I making mistake?

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