[nooonuii]

$p\leftrightarrow q \equiv (p\to q) \wedge (q\to p)$

$~~~~~~~~\equiv (\sim p \vee q)\wedge (\sim q \vee p)$

$~~~~~~~~\equiv (\sim p\wedge \sim q)\vee (\sim p\wedge p)\vee (q\wedge \sim q)\vee (q\wedge p)$

$~~~~~~~~\equiv (\sim p\wedge \sim q)\vee F \vee F \vee (q\wedge p)$

$~~~~~~~~\equiv (\sim p\wedge \sim q)\vee (q\wedge p)$