Checking if a transitive key dependency is in 3rd normal form
A simple check to see if a relation schema is in Third Normal Form is to see if every left hand side of non-trivial functional dependencies is a superkey (and this test can be used also to check if a relation is in Boyce-Codd Normal Form), or, if this is not the case, if every attribute on the right part is a prime attribute (i.e. part of any candidate key).

So in you case both the dependencies A → BCD and BC → A (and also BC → D) have a candidate key as left part, so the schema is in Third Normal Form (and in this case also in the more strict Boyce-Codd Normal Form).