  In this note the Chernoff Theorem is used to approximate evolution semigroups
constructed by the procedure of subordination. The considered semigroups are
subordinate to some original, unknown explicitly but already approximated by
the same method, counterparts with respect to subordinators either with known
transitional probabilities, or with known and bounded L\'evy measure. These
results are applied to obtain approximations of semigroups corresponding to
subordination of Feller processes, and (Feller type) diffusions in Euclidean
spaces, star graphs and Riemannian manifolds. The obtained approximations are
based on explicitly given operators and hence can be used for direct
calculations and computer modelling. In several cases the obtained
approximations are given as iterated integrals of elementary functions and lead
to representations of the considered semigroups by Feynman formulae.
