Self-Distributive Law for Conditional/Formulation 1

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

This can of course be expressed as two separate theorems:

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:
 * $\left({p \implies r}\right) \implies \left({q \implies r}\right) \not \vdash \left({p \implies q}\right) \implies r$