  We consider gravity coupled to a second metric in the strong coupling limit,
where the second kinetic term is absent. This system belongs to the recently
discussed class of models of "gravity with auxiliary fields" by Pani et al. We
prove that, in vacuum, these theories are always equivalent to GR with a
cosmological constant, even in the case where the auxiliary field equations
contain identities leaving undetermined functions. In the situation where some
functions are undetermined, the actual value of the cosmological constant is
dictated by an initial condition, and not by the parameters in the action.
