The need for subtyping in type-systems with dependent types has been realized for some years. But it is hard to prove that systems combining the two features have fundamental properties such as subject reduction. In this paper we investigate a subtyping extension of the system lambdaP, which is an abstract version of the type system of the Edinburgh Logical Framework, LF. By using an equivalent formulation, we establish some important properties of the new system lambdaPsub, including subject reduction. Our analysis culminates in a complete and terminating algorithm which establishes the decidability of type-checking.