\begin{definition}[Definition:Beta-Formula/Table]
From Classification of $\beta$-Formulas, we obtain the following table of $\beta$-formulas $\mathbf B$ and corresponding $\mathbf B_1$ and $\mathbf B_2$:
::$\begin{array}{ccc}
\hline
\mathbf B & \mathbf B_1 & \mathbf B_2\\
\hline
\neg \paren {\mathbf B_1 \land \mathbf B_2} & \neg \mathbf B_1 & \neg \mathbf B_2 \\
\mathbf B_1 \lor \mathbf B_2 & \mathbf B_1 & \mathbf B_2 \\
\mathbf B_1 \implies \mathbf B_2 & \neg \mathbf B_1 & \mathbf B_2 \\
\mathbf B_1 \mathbin \uparrow \mathbf B_2 & \neg \mathbf B_1 & \neg \mathbf B_2 \\
\neg \paren {\mathbf B_1 \mathbin \downarrow \mathbf B_2} & \mathbf B_1 & \mathbf B_2 \\
\neg \paren {\mathbf B_1 \iff \mathbf B_2} & \neg \paren {\mathbf B_1 \implies \mathbf B_2} & \neg \paren {\mathbf B_2 \implies \mathbf B_1} \\
\mathbf B_1 \oplus \mathbf B_2 & \neg \paren {\mathbf B_1 \implies \mathbf B_2} & \neg \paren {\mathbf B_2 \implies \mathbf B_1} \\
\hline
\end{array}$
\end{definition}