Principle of Dilemma/Formulation 2

Theorem

$\vdash \paren {p \implies q} \land \paren {\neg p \implies q} \iff q$

This can be expressed as two separate theorems:

Forward Implication

$\vdash \paren {p \implies q} \land \paren {\neg p \implies q} \implies q$

Reverse Implication

$\vdash q \implies \paren {\paren {p \implies q} \land \paren {\neg p \implies q} }$