  We derive the basic equations of the cosmological first-order post-Newtonian
approximation from the recently formulated fully nonlinear and exact
cosmological perturbation theory in Einstein's gravity. Apparently the latter,
being exact, should include the former, and here we use this fact as a new
derivation of the former. The complete sets of equations in both approaches are
presented without fixing the temporal gauge conditions so that we can use the
gauge choice as an advantage. Comparisons between the two approaches are made.
Both are potentially important in handling relativistic aspects of nonlinear
processes occurring in cosmological structure formation. We consider an ideal
fluid and include the cosmological constant.
