Disjunction of Conjunctions

Theorem

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

Proof

 * align="right" | 3 ||
 * align="right" | 2
 * $p$
 * $\land \mathcal E_1$
 * 2
 * align="right" | 4 ||
 * align="right" | 2
 * $p \lor r$
 * $\lor \mathcal I_1$
 * 3
 * $p \lor r$
 * $\lor \mathcal I_1$
 * 3


 * align="right" | 6 ||
 * align="right" | 5
 * $r$
 * $\land \mathcal E_1$
 * 5
 * align="right" | 7 ||
 * align="right" | 5
 * $p \lor r$
 * $\lor \mathcal I_2$
 * 6
 * align="right" | 8 ||
 * align="right" | 1
 * $p \lor r$
 * $\lor \mathcal E$
 * 1, 2-4, 5-7
 * }
 * align="right" | 1
 * $p \lor r$
 * $\lor \mathcal E$
 * 1, 2-4, 5-7
 * }
 * }