Rule of Addition/Proof Rule

Proof Rule
The rule of addition is a valid argument in types of logic dealing with disjunctions $\lor$.

This includes propositional logic and predicate logic, and in particular natural deduction.

As a proof rule it is expressed in either of the two forms:
 * $(1): \quad$ If we can conclude $\phi$, then we may infer $\phi \lor \psi$.
 * $(2): \quad$ If we can conclude $\psi$, then we may infer $\phi \lor \psi$.

It can be written:
 * $\ds {\phi \over \phi \lor \psi} \lor_{i_1} \qquad \qquad {\psi \over \phi \lor \psi} \lor_{i_2}$