Rule of Idempotence/Conjunction/Formulation 1/Proof

Theorem

 * $p \dashv \vdash p \land p$

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.

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