Conditional is Left Distributive over Disjunction/Formulation 1

Theorem

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

This can be split into two parts:

Forward Implication

$p \implies \paren {q \lor r} \vdash \paren {p \implies q} \lor \paren {p \implies r}$

Reverse Implication

$\paren {p \implies q} \lor \paren{p \implies r} \vdash p \implies \paren {q \lor r}$