Relation in 2NF with a transitive dependency? Tomorrow I have my final exam of Database Design but I have a doubt about the Second Normal Form (2NF).

The definition says a relation is in 2NF if no non-prime attribute is partially dependent on a key.

My doubt is about if a relation could be in 2NF is if has attributes that are fully dependent on a key but transitively.

For example: R (A,B,C,D) with AB key and FD ( AB->C,C->D)

In this case the non-prime attribute C is fully dependent on the key so it meets the condition but in the case of the attribute D I don´t know if it meets the rule. D is dependent on C and due to C is fully dependent on the key,does it mean that D is fully dependent on the key being this relation in 2NF?
The important thing about the 2NF is that in each (non trivial) dependency the determinant should not be a proper subset of a key. In the example, the determinant of AB->C is the full key, while the determinant of C->D is C, which is no part of any key. So the schema is obviously in 2NF.