Proof by Cases/Proof Rule/Tableau Form

Proof Rule
Let $\phi \lor \psi$ be a propositional formula in a tableau proof whose main connective is the disjunction operator.

Let $\chi$ be a propositional formula such that $\left({\phi \vdash \chi}\right)$, $\left({\psi \vdash \chi}\right)$.

The Rule of Or-Elimination is invoked for $\phi \lor \psi$ as follows:

Also defined as
Treatments that refer to this as the Rule of Or-Elimination tend use the abbreviation $\lor \mathcal E$.