  We discuss a generalization of the Ehrenfest theorem to the recently proposed
precanonical quantization of vielbein gravity which proceeds from a space-time
symmetric generalization of the Hamiltonian formalism to field theory.
Classical Einstein-Palatini equations are derived as equations of expectation
values of precanonical quantum operators. The preceding consideration of an
interacting scalar field theory on curved space-time shows how the classical
field equations emerge from the results of precanonical quantization as the
equations of expectation values of the corresponding quantum operators. It also
allows us to identify the connection term in the covariant generalization of
the precanonical Schr\"odinger equation with the spin connection.
