  We obtain the combined mean-field and semiclassical limit from the $N$-body
Schr\"{o}dinger equation for fermions interacting via singular potentials. To
obtain the result, we first prove the uniformity in Planck's constant $h$
propagation of regularity for solutions to the Hartree$\unicode{x2013}$Fock
equation with singular pair interaction potentials of the form $\pm
|x-y|^{-a}$, including the Coulomb and gravitational interactions.
  In the context of mixed states, we use these regularity properties to obtain
quantitative estimates on the distance between solutions to the Schr\"{o}dinger
equation and solutions to the Hartree$\unicode{x2013}$Fock and Vlasov equations
in Schatten norms. For $a\in(0,1/2)$, we obtain local-in-time results when
$N^{-1/2} \ll h \leq N^{-1/3}$. In particular, it leads to the derivation of
the Vlasov equation with singular potentials. For $a\in[1/2,1]$, our results
hold only on a small time scale, or with an $N$-dependent cutoff.
