Biconditional iff Disjunction implies Conjunction

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Theorem

Formulation 1

$p \iff q \dashv \vdash \left({p \lor q}\right) \implies \left({p \land q}\right)$

Formulation 2

$\vdash \left({p \iff q}\right) \iff \left({\left({p \lor q}\right) \implies \left({p \land q}\right)}\right)$