\relax 
\ifx\hyper@anchor\@undefined
\global \let \oldcontentsline\contentsline
\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global \let \oldnewlabel\newlabel
\gdef \newlabel#1#2{\newlabelxx{#1}#2}
\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\bibstyle{plain}
\citation{mendelson}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}About LogiWeb}{2}{subsection.1.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}About the proof system}{2}{subsection.1.2}}
\citation{mendelson}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The new version of the operators}}{3}{figure.1}}
\newlabel{aaa}{{1}{3}{About the proof system\relax }{figure.1}{}}
\citation{mendelson}
\citation{mendelson}
\@writefile{toc}{\contentsline {section}{\numberline {2}The Deduction Algorithm}{4}{section.2}}
\newlabel{support}{{3}{4}{Supporting Lemmas\label {support}\relax }{section.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Supporting Lemmas}{4}{section.3}}
\citation{mendelson}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Corollary $C1.10a$}{5}{subsection.3.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Corollary $C1.10(b)$}{5}{subsection.3.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Lemma ${A1'}^*$}{5}{subsection.3.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Lemma ${A2'}^*$}{5}{subsection.3.4}}
\citation{mendelson}
\citation{mendelson}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Lemma $Double Hypothesis$}{6}{subsection.3.5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.6}Lemma $L1.8$}{6}{subsection.3.6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.7}Lemma $Tautology 1$}{6}{subsection.3.7}}
\citation{mendelson}
\newlabel{main.lemmas}{{4}{7}{The Main Proofs \label {main.lemmas}\relax }{section.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}The Main Proofs }{7}{section.4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Lemma $L3.2(b)'$}{7}{subsection.4.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Lemma $L3.2(c)'$}{7}{subsection.4.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Lemma $L3.2(d)'$}{7}{subsection.4.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Lemma $L3.2(f)'$}{8}{subsection.4.4}}
\newlabel{f.base}{{4.4.1}{8}{The base case of $L3.2(f)'$\label {f.base}\relax }{subsubsection.4.4.1}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.4.1}The base case of $L3.2(f)'$}{8}{subsubsection.4.4.1}}
\newlabel{f.hyp}{{4.4.2}{8}{The induction step of $L3.2(f)'$\label {f.hyp}\relax }{subsubsection.4.4.2}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.4.2}The induction step of $L3.2(f)'$}{8}{subsubsection.4.4.2}}