Factor Principles/Conjunction on Left

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Theorem

Formulation 1

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

Formulation 2

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