Constructive Dilemma

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Theorem

Formulation 1

$p \implies q, r \implies s \vdash p \lor r \implies q \lor s$

Formulation 2

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

Formulation 3

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


Its abbreviation in a tableau proof is $\textrm{CD}$.