First-order general relativity in dimensions () has an internal gauge symmetry that is the higher-dimensional generalization of three-dimensional local translations. We report the extension of this symmetry for -dimensional f (R) gravity with torsion in the Cartan formalism. The new symmetry arises from the direct application of the converse of Noether's second theorem to the action principle of f (R) gravity with torsion. We show that infinitesimal diffeomorphisms can be written as a linear combination of the new internal gauge symmetry, local Lorentz transformations, and terms proportional to the variational derivatives of the f (R) action. It means that the new internal symmetry together with local Lorentz transformations can be used to describe the full gauge symmetry of f (R) gravity with torsion, and thus diffeomorphisms become a derived symmetry in this setting.