Determine third normal form in case of two functional dependencies

Assume I’m given an entity E which has attributes A, B and C, (each of them is a candidate key, but let’s say I can introduce some EID that serves as a PK) with functional dependencies: A determines C and B determines C. How would I get this into a third normal form?

I have tried the following:

E(EID(PK), AID(FK), BID(FK)) A(AID(PK), C) B(BID(PK), C) 

but in this representation, I’m have the attribute C twice in my database. Can anyone advise on a more appropriate way of getting into a third normal form?