The λΠ-calculus modulo theory is an extension of simply typed λ-calculus with dependent types and user-defined rewrite rules. We show that it is possible to replace the rewrite rules of a theory of the λΠ-calculus modulo theory by axioms of equality, when this theory features the notions of proposition and proof, while maintaining the same expressiveness. To do so, we introduce in the target theory a heterogeneous equality. We construct a translation that replaces each use of the conversion rule by the insertion of a transport. To facilitate the proofs, we consider a type system in which conversions are explicitly typed.