you can use the aligned sub-environment from amsmath"
\[
\frac{\begin{aligned}
O&\vdash e_1:T_1 \\ O[T_1/x]&\vdash e_2:T_2
\end{aligned}}%
{O\vdash (let\ ((x e_1))\ e_2):T_2}
\]
(your question ended abruptly, so there may have been more specifications that i wasn't aware of.)
if you wish these lines to be centered, then use gathered rather than aligned (and omit the &s).
both aligned and gathered can accommodate any number of lines, even more than four, although it seems to me that this probably gets too complicated.
remember that the baseline is still relative to the math axis (which is coincident with the fraction rule), so all extra lines will continue to rise above the rest of the displayed expression, and if that part of the expression is in parentheses, the parentheses will be unattractively empty below the line.
$$is obsolete use\[\]instead, see http://tex.stackexchange.com/questions/503/why-is-preferable-to. – bodo Feb 07 '13 at 19:11