Proof by Cases/Sequent Form/Proof 1

Theorem

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

Proof

 * align="right" | 3 ||
 * align="right" | 2
 * $r$
 * By hypothesis
 * 2
 * as $p \vdash r$
 * as $p \vdash r$


 * align="right" | 5 ||
 * align="right" | 4
 * $r$
 * By hypothesis
 * 4
 * as $q \vdash r$
 * as $q \vdash r$