Self-Distributive Law for Conditional/Formulation 2

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

Also see

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

it is not the case that:
 * $\left({p \implies r}\right) \implies \left({q \implies r}\right) \not \vdash \left({p \implies q}\right) \implies r$