The melting temperature ($T_m$) of a solid is generally determined by the pressure applied to it, or indirectly by its density ($n$) through the equation of state. This remains true even for helium solidscite{wilk:67}, where quantum effects often lead to unusual propertiescite{ekim:04}. In this letter we present experimental evidence to show that for a two dimensional (2D) solid formed by electrons in a semiconductor sample under a strong perpendicular magnetic fieldcite{shay:97} ($B$), the $T_m$ is not controlled by $n$, but effectively by the textit{quantum correlation} between the electrons through the Landau level filling factor $ u$=$nh/eB$. Such melting behavior, different from that of all other known solids (including a classical 2D electron solid at zero magnetic fieldcite{grim:79}), attests to the quantum nature of the magnetic field induced electron solid. Moreover, we found the $T_m$ to increase with the strength of the sample-dependent disorder that pins the electron solid.
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