Conditional Elimination

If a conjunction exists, it means that both conjuncts are the case; therefore we can legitimately extract either one of them. Also known as Simplification.

Strategies for constructing proofs in propositional logic
- Next we need to turn our attention to deriving \(L \lor A\). How can we obtain \(L\) ? Well it is contained within the first conjunct of the assumption on line 2. Again, we can get this through the application of Conjunction Elimination. Now, how do we get \(L\) from \((\lnot N \rightarrow L)\)? Well, we already have the antecedent \(\lnot N\) as an assumption on the first line, so we can use Conditional Elimination to derive \(L\). These two steps give us: