Proof by Cases/Formulation 1

Theorem
If both of two alternative cases imply the conclusion, then either one being true is enough to prove the conclusion true.
 * $\left({p \implies r}\right) \land \left({q \implies r}\right) \dashv \vdash \left({p \lor q}\right) \implies r$

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

This can be expressed as two separate theorems:

Also known as
This theorem is sometimes known as the derived rule of separation of cases.

Also see

 * Principle of Dilemma