  We show that if two 4-dimensional metrics of arbitrary signature on one
manifold are geodesically equivalent (i.e., have the same geodesics considered
as unparameterized curves) and are solutions of the Einstein field equation
with the same stress-energy tensor, then they are affinely equivalent or flat.
Under the additional assumption that the metrics are complete or the manifold
is closed, the result survives in all dimensions >2.
