newtonian mechanics - Strong Newton's third law of action and reaction: Mathematical Interpretation

According to the strong law of action and reaction for internal forces (Goldstein):

$\mathbf F_\mathrm {ij}=-\mathbf F_\mathrm{ji}$ and the forces lie along the direction joining the particles.

Now consider the statement

If those internal forces are conservative we can associate the internal forces with a potential of the form $V_\textrm{ij}(|\mathbf{r_i}-\mathbf{r_j}|)$.

How can one justify this statement mathematically though it seems intuitively obvious?