Before revision: In logic, Birkhoff's theorem states that an equality t = u is a semantic consequence of a set of equalities E, if and only if t = u can be proven from the set of equalities .
After revision: in equational logicIn logic, Birkhoff's theorem states that an equality t = u is a semantic consequence of a set of equalities E, if and only if t = u can be proven from the set of equalities .