Conjunction Equivalent to Negation of Implication of Negative

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Theorems

Formulation 1

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

Formulation 2

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