  For the two-species Vlasov-Maxwell-Boltzmann (VMB) system with the scaling
under which the moments of the fluctuations to the global Maxwellians formally
converge to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell (NSFM)
system with Ohm's law, we prove the uniform estimates with respect to Knudsen
number $\eps$ for the fluctuations. As consequences, the existence of the
global in time classical solutions of VMB with all $\eps \in (0,1]$ is
established. Furthermore, the convergence of the fluctuations of the solutions
of VMB to the classical solutions of NSFM with Ohm's law is rigorously
justified.
  This limit was justified in the recent breakthrough of Ars\'enio and
Saint-Raymond \cite{Arsenio-SRM-2016} from renormalized solutions of VMB to
dissipative solutions of incompressible viscous electro-magneto-hydrodynamics
under the corresponding scaling. In this sense, our result gives a classical
solution analogue of the corresponding limit in \cite{Arsenio-SRM-2016}.
