  This paper completes the argument that lattice simulations of partially
quenched QCD can provide quantitative information about QCD itself, with the
aid of partially quenched chiral perturbation theory. A barrier to doing this
has been the inclusion of $\Phi_0$, the partially quenched generalization of
the $\eta'$, in previous calculations in the partially quenched effective
theory. This invalidates the low energy perturbative expansion, gives rise to
many new unknown parameters, and makes it impossible to reliably calculate the
relation between the partially quenched theory and low energy QCD. We show that
it is straightforward and natural to formulate partially quenched chiral
perturbation theory without $\Phi_0$, and that the resulting theory contains
the effective theory for QCD without the $\eta'$. We also show that previous
results, obtained including $\Phi_0$, can be reinterpreted as applying to the
theory without $\Phi_0$. We contrast the situation with that in the quenched
effective theory, where we explain why it is necessary to include $\Phi_0$.
  We also compare the derivation of chiral perturbation theory in partially
quenched QCD with the standard derivation in unquenched QCD. We find that the
former cannot be justified as rigorously as the latter, because of the absence
of a physical Hilbert space. Finally, we present an encouraging result:
unphysical double poles in certain correlation functions in partially quenched
chiral perturbation theory can be shown to be a property of the underlying
theory, given only the symmetries and some plausible assumptions.
