Factor Principles/Disjunction on Right

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Theorem

Formulation 1

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

Formulation 2

$\vdash \left({p \implies q}\right) \implies \left({\left({p \lor r}\right) \implies \left ({q \lor r}\right)}\right)$