¬P∨¬Q⇒¬(P∧Q)

証明

https://scrapbox.io/files/65f29c24974fd8002333b160.svg

code:proof.tikz(tex)

\usepackage{fitch}

\usepackage{amsmath}

\begin{document}

$\Large\begin{nd}

\hypo {s} {\lnot P\lor\lnot Q}

\open

\hypo {h} {P\land Q}

\open

\hypo {np} {\lnot P}

\have {np2} {P} \ae{h}

\have {np3} {\bot} \ne{np,np2}

\close

\open

\hypo {nq} {\lnot Q}

\have {nq2} {Q} \ae{h}

\have {nq3} {\bot} \ne{nq,nq2}

\close

\have {b} {\bot} \oe{s,np-np3,nq-nq3}

\close

\have {g} {\lnot(P\land Q)} \ii{h-b}

\end{nd}$

\end{document}