  In this work, we present the first, to our knowledge, theoretical description
of two-proton removal reactions with proton target $(p,3p)$ for medium-mass
nuclei at intermediate energies and present cross sections for the different
bound states of the residual nucleus with two fewer protons. The description of
the reaction assumes two sequential ``quasifree'' collisions between the target
and removed protons and considers eikonal propagation in between. The formalism
is applied to the reactions $^{12}\mathrm{C}(p,3p)^{10}\mathrm{Be}$,
$^{28}\mathrm{Mg}(p,3p)^{26}\mathrm{Ne}$ and
$^{54}\mathrm{Ca}(p,3p)^{52}\mathrm{Ar}$, finding reasonable agreement to
experimental data for the $^{12}$C target and an overestimation of a factor
$\sim3$ for the more neutron-rich and $^{54}$Ca, which is similar to the
results found in two-proton knockout experiments with $^9$Be and $^{12}$C
targets.
