Conjunction of Disjunctions with Complements implies Disjunction

Theorem

 * $\left({p \lor r}\right) \land \left({q \lor \neg r}\right) \vdash p \lor q$

Proof

 * align="right" | 6 ||
 * align="right" | 1
 * $\neg r \lor q$
 * Sequent Introduction
 * 5
 * Rule of Commutation
 * align="right" | 7 ||
 * align="right" | 1
 * $r \implies q$
 * Sequent Introduction
 * 6
 * Rule of Material Implication
 * 6
 * Rule of Material Implication