$\equiv$ Theorem 1: true

$\hspace{2 cm} true \equiv p \equiv p$, Axiom, Identity of $\equiv$,
$\hspace{0.5 cm} =$ Leibniz, E = Identity Axiom above, $p = p \equiv p, q = true$
$\hspace{2 cm} true \equiv true$
$\hspace{0.5 cm} \equiv$ Axiom, Identity of $\equiv$,$true \equiv p \equiv p$,
$\hspace{2 cm}$ true