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These are rules in implication form. 
\begin{align}
&(Rule) &&(From) &&(To\,\,infer)\notag\\
&1.\,MP &&p,\,\,p\to q &&q\notag\\
&2.\,MT &&\sim q \to p,\,\,\sim p && q \notag\\
&3.\,DS &&p\vee q,\,\,\sim p && q \notag\\
&4.\,Simp &&p\cdot q && p \notag\\
&5.\,Conj &&p,\,\,q &&p\cdot q \notag\\
&6.\,HS &&p\to q,\,\, q\to r &&p\to r \notag\\
&7.\,Add &&p &&p\vee q \notag\\
&8.\,CD &&p\to r,\,\, q\to r,\,\, p\vee q &&r \notag
\end{align}

These are rules in equivalence form.
\begin{align}
&(Rule) &&(Original form) &&:: &&(Equivalence form) \notag\\
9.\,&DN &&p &&:: &&\sim\sim p \notag\\
10.\,&DeM &&\sim (p\cdot q) &&:: &&\sim p\vee \sim q \notag\\
&DeM &&\sim (p\vee q) &&:: &&\sim p\cdot \sim q \notag\\
11.\,&Comm &&p\vee q &&:: &&q\vee p \notag\\
&Comm &&p\cdot q &&:: &&q\cdot p \notag\\
12.\,&Asc &&p\vee (q\vee r) &&:: &&(p\vee q)\vee r \notag\\
&Asc &&p\cdot (q\cdot r) &&:: &&(p\cdot q)\cdot r \notag\\
13.\,&Dist &&p\cdot (q\vee r) &&:: &&(p\cdot q)\vee (p\cdot 
r) \notag\\
&Dist &&p\vee (q\cdot r) &&:: &&(p\vee q)\cdot (p\vee r) 
\notag\\
14.\,&Ctra &&p\to q &&:: &&\sim q\,\,\to\,\, \sim p \notag\\
15.\,&Impl &&p\to q &&:: &&\sim p\vee q \notag\\
16.\,&Exp &&(p\cdot q)\to r &&:: &&p\to (q\to r) \notag\\
17.\,&Taut &&p &&:: &&p\cdot p \notag\\
&Taut &&p &&:: &&p\vee p \notag\\
18.\,&Equi &&p\equiv q &&:: &&(p\to q)\cdot (q\to p) \notag\\
&Equi &&p\equiv q &&:: &&(p\cdot q)\vee (\sim p\cdot\sim q) 
\notag
\end{align}
\end{document}