A semiring variety is \emph{d-semisimple} if it is generated by the distributive lattice of order two and a finite number of finite fields. A d-semisimple variety ${\mathbf V}={\bf HSP}\{B_2,F_1,\dots,F_{k}\}$ plays the main role in this paper. It will be proved that it is finitely based, and that, up to isomorphism, the two-element distributive lattice $B_2$ and all subfields of $F_1,\dots,F_k$ are the only subdirectly irreducible members in it.