Principle of Composition/Formulation 1
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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
- $\paren {p \land q} \implies r \vdash \paren {p \implies r} \lor \paren {q \implies r}$