Contracting tensors λ with ν in the Bianchi identities R_(λμνκ;η) + R_(λμην;κ) + R_(λμκη;ν) = 0 gives R_(μκ;η) - R_(μη;κ) + R^ν _(μκη;ν) = 0. Contracting again, R_(;η) - R^μ _(η;μ) - R^ν _(η;ν) = 0, or (R^μ _η - 1/2 δ^μ _η R)_(;μ) = 0, or (R^μν - 1/2 g^μν R)_(;μ) = 0.