Rule of Idempotence/Disjunction/Formulation 1/Proof by Truth Table

Theorem

 * $p \dashv \vdash p \lor p$

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connectives match for each boolean interpretations.

$\begin{array}{|c||ccc|} \hline p & p & \lor & p \\ \hline T & T & T & T \\ F & F & F & F \\ \hline \end{array}$