Law of Identity/Formulation 2/Proof by Truth Table

Theorem

 * $\vdash p \implies p$

Proof
We apply the Method of Truth Tables to the proposition.

As can be seen by inspection, the truth value under the main connective is $T$ throughout.

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