Prove that a relation which is 4nf must be bcnf, Database Management System

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Prove that a relation which is 4NF must be BCNF.  

Ans Let R be in 4NF.  Suppose it is not in BCNF.  Hence, there exists an FD X→Y in R such that x is not a super key. Although by the rule M1 X→Y|=x→→Y. Once again x here is not a super key.  This contradicts the fact that R is in 4NF.  Hence, our assumption is false.  Each R in 4NF should be in BCNF.


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