We prove that the quantum-mechanical ground state energy of a system consisting of an arbitrary number, M, of static nuclei of atomic number ≤Z and of an arbitrary number, N, of Pauli electrons interacting with the quantized, ultraviolet-cutoff radiation field is bounded below by $-K.M, where K is a finite constant depending on Z, on the finestructure constant α and on the ultraviolet cutoff Λ, with , as , and K' independent of Λ.