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I'm using lplfitch.sty to produce Fitch-style natural deduction proofs. I want to use different symbols from the ones that are predefined. Specifically, I want to use \sim instead of \neg for negation, and \supset instead of \rightarrow for the conditional. How can I change these?

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The command you don't like is defined with a simple \newcommand:

\newcommand*\lif{\rightarrow}

Just modify it definitions to suit your tastes:

\renewcommand*\lif{\supset}

You'll next want to redefine \lnot:

\renewcommand*\lnot{\mathord{\sim}}

(note that \mathord is necessary as \sim is considered a binary relation symbol otherwise).

\documentclass{article}
\usepackage{lplfitch}

\renewcommand*\lif{\supset}
\renewcommand*\lnot{\mathord{\sim}}

\begin{document}

$\uni{x}{\exi{y}{(P(x)\lif \lnot Q(x,y))}}$

\end{document}

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