Self-Distributive Law for Conditional/Formulation 2

Theorem
The following is known as the Self-Distributive Law:
 * $\vdash \paren {p \implies \paren {q \implies r} } \iff \paren {\paren {p \implies q} \implies \paren {p \implies r} }$

Also see

 * Conditional is not Left Self-Distributive where it is shown that while:
 * $\paren {p \implies q} \implies r \vdash \paren {p \implies r} \implies \paren {q \implies r}$

it is not the case that:
 * $\paren {p \implies r} \implies \paren {q \implies r} \vdash \paren {p \implies q} \implies r$