Exportation and Self-Conditional

Theorem

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

Proof

From the Rule of Exportation:

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

Then by Self-Distributive Law for Conditional:

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

$\blacksquare$