
Originally Posted by
Plato
I for one am not so sure about that. It is not standard.
$\displaystyle \begin{gathered} 1.\,\left( {\neg p \vee q} \right) \to r \hfill \\
2.\,r \to \left( {s \vee t} \right) \hfill \\ 3.\,\neg s \wedge \neg u \hfill \\
4.\,\neg u \to \neg t \hfill \\ \therefore \,p \hfill \\ \end{gathered} $
$\displaystyle \begin{gathered}
5.\,\left( {\neg p \vee q} \right) \to \left( {s \vee t} \right)\;\left[ {1\,\& \,2} \right] \hfill \\
6.\,\neg u\;\left[ 3 \right] \hfill \\
7.\,\neg t\;\left[ 4 ,\& \,6\right] \hfill \\
8.\,\neg s\;\left[ 3 \right] \hfill \\
9.\,\neg s \wedge \neg t\left[ {7\,\& \,8} \right] \hfill \\
\end{gathered} $
$\displaystyle \begin{gathered} 10.\,\neg \left( {s \vee t} \right)\left[ 9 \right] \hfill \\ 11.\,\neg \left( {\neg p \vee q} \right)\left[ {10\,\& \,5} \right] \hfill \\ 12.\,p \wedge \neg q\left[ {11} \right] \hfill \\ \therefore \,p\left[ {12} \right] \hfill \\ \end{gathered} $
I will leave it to you to supply the reasons by name. Names of the rules differ from text to text and author to author. That is the reason I don’t trust what you have handed. I have taught this material for years in North America. I can tell you that I got confused each time we changed textbooks.
Notations and rules names are simply not standard.
However, the layout of the proof that I have given you is fairly standard.