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\begin{document}

\title{Soundness and Completeness of Implicational Logic}
\author{Asta Halkjær From \and Jørgen Villadsen}
\maketitle

\tableofcontents

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\begin{abstract}
This work is a formalization of soundness and completeness of the Bernays-Tarski axiom system for classical implicational logic. The completeness proof is constructive following the approach by László Kalmár, Elliott Mendelson and others. The result can be extended to full classical propositional logic by uncommenting a few lines for falsehood.
\end{abstract}

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\end{document}

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