We show that in quantum electrodynamics the Green functions of the Dirac-dressed fermion coincide, for any value of the gauge parameter in the $R_{\xi }$ gauge and to all orders in perturbation theory, with those of the undressed fermion in the Landau gauge. The dressed fermion couples only to the transverse photon, and the gauge parameter is confined to a decoupled sector. The dressed vertex then obeys a homogeneous Ward identity, and the dressed field is renormalized multiplicatively with no new counterterm. A partially dressed family realizes the Landau–Khalatnikov–Fradkin relation exactly, and dressings with other kernels reproduce other gauges. Every dressing yields the same pole mass and, with the differences carried by the vertex, the same mass function.