Biconditional iff Disjunction implies Conjunction

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Theorem

Formulation 1

$p \iff q \dashv \vdash \paren {p \lor q} \implies \paren {p \land q}$

Formulation 2

$\vdash \paren {p \iff q} \iff \paren {\paren {p \lor q} \implies \paren {p \land q} }$