In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced $m_1$-system and $m_2$-system in semiring. We have shown that if Q is an ideal in the semiring R and if M is an $m_2$-system of R such that $overline{Q}{igcap}M={emptyset}$ then there exists as 2-prime ideal P of R such that Q $subseteq$ P with $P{igcap}M={emptyset}$.