Biconditional is Reflexive

Theorems
Equivalence, considered as a relation, is reflexive:
 * $p \iff p \dashv \vdash \top$

This can otherwise be stated as that equivalence destroys copies of itself.

Proof by Natural Deduction
The theorem:
 * $p \iff p \dashv \vdash \top$

is the Law of Identity.

Proof by Truth Table
We apply the Method of Truth Tables.

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

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