Can I typeset a proof tree in exercise 2.4.3(c) from mathematical logic by ian chiswell and wilfrid hodges(2007) with tex?

Question

The picture below is exercise 2.4.3(c).

Answer 1

There are several packages to draw proof trees in LaTeX, e.g., bussproofs, ebproof,prftrees. Here is a solution using bussproofs to draw the proof tree and cancel to slash one of the assumption.

\documentclass[11pt]{article}
\usepackage{bussproofs}
\usepackage{cancel}
\begin{document}
\begin{prooftree}
\AxiomC{\qquad\textcircled{\scriptsize1}}
  \noLine
  \UnaryInfC{$\cancel\psi$}
\AxiomC{$\phi\wedge\psi$}
  \RightLabel{($\wedge$E)}
  \UnaryInfC{$\phi$}
    \RightLabel{($\wedge$I).}
    \insertBetweenHyps{\hskip2cm}
    \BinaryInfC{$(\psi\wedge\phi)$}
      \LeftLabel{\textcircled{\scriptsize 1}}
      \RightLabel{($\rightarrow$I)}
      \UnaryInfC{$(\psi\rightarrow(\psi\wedge\phi))$}
\end{prooftree}
\end{document}

Resulting in

With ebproof the same proof tree can be achieved with the following code

\documentclass[11pt]{article}

\usepackage{ebproof}
\usepackage{cancel}

\begin{document}
\begin{prooftree}[template=$\inserttext$]
\Hypo{\quad\textcircled{\scriptsize 1}}
\Infer[no rule]1{\cancel\psi}
\Hypo{(\phi\wedge\psi)}
\Infer1[($\wedge$E)]{\phi}
\Infer[separation=2cm]2[($\wedge$I)]{(\psi\wedge\phi)}  
\Infer[left label=\textcircled{\scriptsize 1}, 
       right label=($\rightarrow$I)]1{(\psi\rightarrow(\psi\wedge\phi))}
\end{prooftree}

\end{document}

Answer 2

With the help of bussproofs and cancel:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{bussproofs}
\usepackage{cancel}

\newcommand{\lto}{\mathbin{\to}}

\begin{document}

\begin{prooftree}
\renewcommand{\defaultHypSeparation}{\hspace{4em}}
\AxiomC{${\cancel{\psi}}^{\,\raisebox{\depth}{\textcircled{\footnotesize 1}}}$}
\AxiomC{$(\phi\land\psi)$}
\RightLabel{($\land\mathrm{E}$)}
\UnaryInfC{$\phi$}
\RightLabel{($\land\mathrm{I}$)}
\BinaryInfC{$(\psi\land\phi)$}
\LeftLabel{\textcircled{\footnotesize 1}}
\RightLabel{($\lto\mathrm{I}$)}
\UnaryInfC{$(\psi\lto(\psi\land\phi))$}
\end{prooftree}

\end{document}