Definition:Alpha-Formula/Table

Definition
From Classification of $\alpha$-Formulas, we obtain the following table of $\alpha$-formulas $\mathbf A$ and corresponding $\mathbf A_1$ and $\mathbf A_2$:


 * $\begin{array}{ccc}

\hline \mathbf A & \mathbf A_1 & \mathbf A_2\\ \hline

\neg\neg \mathbf A_1 & \mathbf A_1 & \\ \mathbf A_1 \land \mathbf A_2 & \mathbf A_1 & \mathbf A_2 \\ \neg \left({\mathbf A_1 \lor \mathbf A_2}\right) & \neg \mathbf A_1 & \neg \mathbf A_2 \\ \neg \left({\mathbf A_1 \implies \mathbf A_2}\right) & \mathbf A_1 & \neg \mathbf A_2 \\ \neg \left({\mathbf A_1 \mathbin \uparrow \mathbf A_2}\right) & \mathbf A_1 & \mathbf A_2 \\ \mathbf A_1 \mathbin \downarrow \mathbf A_2 & \neg \mathbf A_1 & \neg \mathbf A_2 \\ \mathbf A_1 \iff \mathbf A_2 & \mathbf A_1 \implies \mathbf A_2 & \mathbf A_2 \implies \mathbf A_1 \\ \neg \left({\mathbf A_1 \oplus \mathbf A_2}\right) & \mathbf A_1 \implies \mathbf A_2 & \mathbf A_2 \implies \mathbf A_1 \\

\hline \end{array}$