Implication is Left Distributive over Disjunction

Theorem

Formulation 1

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

Formulation 2

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