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:


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