  We prove that any regular Casimir in 3D magnetohydrodynamics is a function of
the magnetic helicity and cross-helicity. In other words, these two helicities
are the only independent regular integral invariants of the coadjoint action of
the MHD group $\text{SDiff}(M)\ltimes\mathfrak X^*(M)$, which is the semidirect
product of the group of volume-preserving diffeomorphisms and the dual space of
its Lie algebra.
