Although I am unfamiliar with the context, you can use an array
to brake the "antecedents" into separate lines:
\documentclass{article}
\begin{document}
\[
\frac{\begin{array}{@{}c@{}}
A \rightarrow f[\overrightarrow{B}]:= \Psi \\
\Phi \in \langle\Psi\rangle
\end{array}}{
A \rightarrow f[\bullet\overrightarrow{B}];\Phi}
\]
\end{document}
This will place the object centred vertically around the fraction line. If that is not of concern, you can do everything inside an array
environment:
\[
\begin{array}{c}
A \rightarrow f[\overrightarrow{B}]:= \Psi \\
\Phi \in \langle\Psi\rangle \\
\hline
A \rightarrow f[\bullet\overrightarrow{B}];\Phi
\end{array}
\]
There are other packages that also provide inference rule functionality, like semantic
or proofs
.