  Using the fully nonlinear and exact perturbation formulation with
magnetohydrodynamics (MHD) in Minkowski background we derive first-order
post-Newtonian (1PN) equations without imposing the slicing (temporal gauge)
condition. The 1PN MHD formulation is complementary to our recently presented
fully relativistic MHD combined with 0PN gravity available only in the maximal
slicing. We present the 1PN MHD equations in two gauge conditions previously
used in the literature and provide gauge transformation relations between
different gauges. We derive the PN effects on MHD waves in a static homogeneous
medium.
