Even if you know equivalences between formulas, it's much better if you don't use them. For instance, if you have to write the negation of , don't write directly, but .
Understand that not everything is so obvious as it seems, and that someone may ask you to prove things like , where if you could use those simplifications, you would do almost no work.
Another example: going from in one line to having in the next can't be justified with any of the 9 rules. But if you succeed in proving and understanding that , then maybe you can add that as an additional rule to use in future demonstrations. I will give some of these in the next section.