In some books or tutorials more rules are allowed (apart from the basic 9) in order to deal with formulas more easily. They represent an abstraction: stop working in the details to dedicate our work in more complex problems (it's like the high level programming languages).

If you decide to use them, you will lose a lot of interesting work to do, but you will finish faster. My advice is to only use a rule if you know how to prove its validity by using the 9 basic rules.

Some of the ones I found at several places are:

- Law of double negation: allows changing to and viceversa.
- Modus Tollens: having and , then .
- Disjunctive syllogism: if and , then . And if and , then it's .
- Elimination of : if you have , then happen both and .
- Elimination of : if you have , then , and also .
- Elimination of : if you have , then .
- Theorems which you can use when you want: , , and more.
- Change of equivalent formulas: if , then where it says you can put and viceversa.

Daniel Clemente Laboreo 2005-05-17