Factor Principles/Disjunction on Right

Theorem

Formulation 1

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

Formulation 2

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