Exportation and Self-Conditional

Theorem

$p \land q \implies r \dashv \vdash \paren {p \implies q} \implies \paren {p \implies r}$

Proof

From the Rule of Exportation:

$\paren {p \land q} \implies r \dashv \vdash p \implies \paren {q \implies r}$

Then by Self-Distributive Law for Conditional:

$p \implies \paren {q \implies r} \dashv \vdash \paren {p \implies q} \implies \paren {p \implies r}$

$\blacksquare$