  We show that a stationary solution of the Einstein-Maxwell equations which is
close to a non-degenerate Reissner-Nordstr\"om-de Sitter solution is in fact
equal to a slowly rotating Kerr-Newman-de Sitter solution. The proof uses the
non-linear stability of the Kerr-Newman-de Sitter family of black holes for
small angular momenta, recently established by the author, together with an
extension argument for Killing vector fields. Our black hole uniqueness result
only requires the solution to have high but finite regularity; in particular,
we do not make any analyticity assumptions.
