We study the semiring variety $mathbf{V}$ generated by any finite number of finite fields $F_1,dots,F_k$ and two-element distributive lattice $B_2$, i.e., $mathbf{V}=operatorname{HSP}{B_2,F_1,dots,F_k}$. It is proved that $mathbf{V}$ is hereditarily finitely based, and that, up to isomorphism, $B_2$ and all subfields of $F_1,dots,F_k$ are the only subdirectly irreducible semirings in $mathbf{V}$.
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