Copi's 19 rules of inference are like the multiplication table. If you memorize a few basic multiplications, then you can use them as tools to compute any complex multiplication. However, if you were superhuman, you could memorize every one of the infinity of correct multiplications so that you would never have to compute any. Similarly, by using a finite set of rules of inference, you prove every complex argument to be valid. A proof is successful if each step is justified by one of our rules of inference, and if the last step is the proposition to be proven.
Elegance is desirable, but only validity is essential.
Strategy tips for constructing proofs Be sure that you have translated or copied the problem correctly. If you make a mistake, then you may have written down an invalid argument. Similarly, make sure the argument is valid. Don't make up problems at random except for adventure. Know the rules of inference and replacement intimately.