The seminal work of Jan Rutten on a description of systems as coalgebras included also the possibility to specify a class of systems via coequations, the dual concept to equational specification of a class of algebras. A coequation is a subset of a cofree coalgebra - and a system satisfies the coequation iff it is injective w.r.t. the subset. This is dual to equations expressed via a congruence of a free algebra (and projectivity expressing that the equations are satisfied). We now develop a logic of coequations by formulating two simple inference rules, and proving that they are sound and complete. As a consequence, we dualize Birkhoff's characterization of equational theories as precisely the fully invariant congruences of the free algebra: we prove that a subset of a cofree coalgebra is a theory iff it is a fully invariant subcoalgebra.