Chapter 5, Tutorial 5
Derived Rules: Helpful Shortcuts

In an advanced logic class, one might prove that the rules we've already given are quite sufficient to prove any valid argument as valid by derivation. (The derivations are enough, you don't need truth tables any longer; hooray!)

So, our rules all trustworthy -- none will go from true input to false output -- and they also form a set complete enough to prove any valid argument valid. Put another way, we have all the essential rules.

Still, you may still think of further rules you might want to have, rules that are trustworthy, and will allow you to short-cut derivations. These are optional rules but very helpful in practice.

Here's an obvious sort of situation illustrating how it would be nice to have more rules.