Law of Excluded Middle/Sequent Form/Proof by Truth Table

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 $p$.

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