Uniqueness of Kerr-Newman-de Sitter black holes with small angular momenta

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.