  In this paper, the Liouville-type theorems for the steady Navier-Stokes
system are investigated. First, we prove that any bounded smooth helically
symmetric solution in $\mathbb{R}^3$ must be a constant vector. Second, for
steady Navier-Stokes system in a slab supplemented with Navier boundary
conditions, we prove that any bounded smooth solution must be zero if either
the swirl or radial velocity is axisymmetric, or $ru^{r}$ decays to zero as $r$
tends to infinity. Finally, when the velocity is not big in $L^{\infty}$-space,
the general three-dimensional steady Navier-Stokes flow in a slab with the
Navier boundary conditions must be a Poiseuille type flow. The key idea of the
proof is to establish Saint-Venant type estimates that characterize the growth
of Dirichlet integral of nontrivial solutions.
