---
tags:
  - propositional-logic
  - logic
---

# Disjunction Elimination

This rule is sometimes also referred to as _Constructive Dilemma_. This can be a
bit tricky to understand because the goal is to derive or _introduce_ a new
proposition separate from the disjunction you start out with. This may be
disjunction, a single proposition or a proposition containing any other logical
connective. You do this by constructing two sub-proofs, one for each of the
disjuncts comprising the disjunction you start out with. If you can derive your
target proposition as the conclusion of each subproof then you may invoke the
conclusion in the main proof and take it to be derived.

![](/img/disjunc-elim.png)

_Here is an example where Disjunction Elimination is used to derive a new
disjunction._

![](/img/proofs-drawio-Page-6.drawio.png)

_Here are two further examples that use Disjunction Elimination to derive
singular propositions_

![](/img/ORelim1.png) ![](/img/ORelim2.png)
