Rule of Idempotence/Disjunction/Formulation 1/Proof by Truth Table
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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.
$\begin{array}{|c||ccc|} \hline p & p & \lor & p \\ \hline \T & \T & \T & \T \\ \F & \F & \F & \F \\ \hline \end{array}$
$\blacksquare$