Biconditional is Reflexive/Proof 2

Theorem

$\vdash p \iff p$

Proof

We apply the Method of Truth Tables.

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

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

$\blacksquare$