Law of Excluded Middle/Sequent Form/Proof 2

Theorem

The Law of Excluded Middle can be symbolised by the sequent:

$\vdash p \lor \neg p$

Proof

We apply the Method of Truth Tables to the proposition $\vdash p \lor \neg p$.

As can be seen by inspection, the truth value of the main connective, that is $\lor$, is $T$ for each boolean interpretation for $p$.

$\begin{array}{|cccc|} \hline p & \lor & \neg & p \\ \hline F & T & T & F \\ T & T & F & T \\ \hline \end{array}$

$\blacksquare$