6.5 Skip steps

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 $\neg P$, don't write $P$ directly, but $\neg\neg P$.

Understand that not everything is so obvious as it seems, and that someone may ask you to prove things like $P\vdash\neg\neg P$, where if you could use those simplifications, you would do almost no work.

Another example: going from $\neg(A\vee B)$ in one line to having $\neg A\wedge\neg B$ in the next can't be justified with any of the 9 rules. But if you succeed in proving and understanding that $\neg(A\vee B)\vdash\neg A\wedge\neg B$, 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.