We show the soundness of a λ-calculus ℬ where de Bruijn indices are used, substitution is explicit, and reduction is step-wise. This is done by interpreting ℬ in the classical calculus where the explicit substitution becomes implicit and de Bruijn indices become named variables. This is the first flat semantics of explicit substitution and step-wise reduction and the first clear account of exactly when α-reduction is needed.