# Implication Equivalent to Negation of Conjunction with Negative

## Theorem

#### Formulation 1

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

#### Formulation 2

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