\begin{frame} \frametitle{Derivation with Natural Deduction} \begin{exampleblock}{Derivation with Natural Deduction} Can we derive \quad$q \wedge \neg r$\quad from \quad$(p \wedge q) \wedge \neg r$\quad? \pause\bigskip \begin{tikzpicture} \naturaldeduction{ \proofstep{$(p \wedge q) \wedge \neg r$}{premise}; \mpause[1]{ \proofstep{$p \wedge q$}{$\wedge_{e_1}$ 1}; } \mpause{ \proofstep{$q$}{$\wedge_{e_2}$ 2}; } \mpause{ \proofstep{$\neg r$}{$\wedge_{e_2}$ 1}; } \mpause{ \proofstep{$q \wedge \neg r$}{$\wedge_{i}$ 3, 4}; } } \end{tikzpicture} \pause\pause\pause\pause\pause \bigskip Hence we have derived \begin{talign} (p \wedge q) \wedge \neg r \quad\vdash\quad q \wedge \neg r \end{talign} \end{exampleblock} \end{frame}