Principle of Composition/Formulation 1

Theorem

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

This can be split into two parts:

Forward Implication

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

Reverse Implication

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