Self-Distributive Law for Conditional/Formulation 1

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

This can of course be expressed as two separate theorems:

Also see

 * Conditional is not Right 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:
 * $\paren {p \implies r} \implies \paren {q \implies r} \not \vdash \paren {p \implies q} \implies r$