\documentclass{article}
\usepackage{argoclp}
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\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
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\begin{document}

\title{High school geometry theorems}
\author{Hilbert's axiomatic system.\\
Formalized by: Sana Stojanovic Djurdjevic \\
Proved by: ArgoGeoChecker.}
\date{30.03.2018.}
\maketitle

\begin{theorem}[th_1_04.]
Assuming that $A \not \in p$ and $B \neq C$ and $B \in p$ and $C \in p$ and $\neg col(A, B, C)$ and $A \in \alpha$ and $B \in \alpha$ and $C \in \alpha$ it holds that $p \in \alpha$ and $A \in \alpha$.
\end{theorem}

{\em Proof:}
\setcounter{proofstepnum}{0} 


\proofstep{0} {From the facts $B \neq C$ and $B \in p$ and $C \in p$ and $B \in \alpha$ and $C \in \alpha$ it holds that $p \in \alpha$ (using $ax_I6$).} 

\proofstep{0} {The conclusion follows from the facts $p \in \alpha$ and $A \in \alpha$.} 
QED
\hrule 

\end{document}
