Principle of Dilemma/Formulation 2
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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
- $\vdash q \implies \paren {\paren {p \implies q} \land \paren {\neg p \implies q} }$