Bussproofs example LaTeX

\def\defaultHypSeparation{\hskip .05in}
\begin{prooftree}
                        \AXC{(Ax)}
                    \alwaysNoLine
                    \UIC{$A \Rightarrow A$}
                \LeftLabel{$LW$}
                \alwaysSingleLine
                \UIC{$A, C \Rightarrow A$}
            \LeftLabel{$RW^*$}
            \UIC{$A, C \Rightarrow B, A, A$}
                        \AXC{(Ax)}
                    \alwaysNoLine
                    \UIC{$B \Rightarrow B$}
                \alwaysSingleLine
                \RightLabel{$RW$}
                \UIC{$B \Rightarrow B, A$}
            \RightLabel{$LW^*$}
            \UIC{$A, B, C \Rightarrow B, A$}
        \LeftLabel{$L \rightarrow$}
        \BIC{$A, A \rightarrow B, C \Rightarrow B, A$}
    \LeftLabel{$R \vee$}
    \UIC{$A, A \rightarrow B, C \Rightarrow B \vee A$}
                    \AXC{(Ax)}
                \alwaysNoLine
                \UIC{$A \Rightarrow A$}
            \alwaysSingleLine
            \LeftLabel{$RW^*$}
            \UIC{$A \Rightarrow A, B, A, C$}
                        \AXC{(Ax)}
                    \alwaysNoLine
                    \UIC{$B \Rightarrow B$}
                \alwaysSingleLine
                \RightLabel{$LW$}
                \UIC{$A, B \Rightarrow B$}
            \RightLabel{$RW^*$}
            \UIC{$A, B \Rightarrow B, A, C$}
        \RightLabel{$L \rightarrow$}
        \BIC{$A, A \rightarrow B \Rightarrow B, A, C$}
    \RightLabel{$R \vee$}
    \UIC{$A, A \rightarrow B \Rightarrow B \vee A, C$}
\RightLabel{$Cut$}
\BIC{$A, A \rightarrow B \Rightarrow B \vee A$}
\end{prooftree}
\def\defaultHypSeparation{\hskip .2in}