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I would like to use something like \crefrange{ref1}{ref2} where ref1 and ref2 are arguments of \label statements for equations numbered 1 and 5, respectively. But instead of showing equations (1) to (5), I would like to show only: (1) to (5). How can I accomplish this?

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The cleveref package provides the \labelcref macro, which acts just like \cref except that the name of the counter of the objects being cross-referenced is omitted.

Note that whereas the arguments of \cref needn't all refer to the same counter, that's not true for the \labelcref (as well as for \crefrange).

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\documentclass{article}
\usepackage[noabbrev]{cleveref}
\begin{document}
\refstepcounter{equation} \label{ref1} % short-hand method
\refstepcounter{equation} \label{ref2}
\refstepcounter{equation} \label{ref3}
\refstepcounter{equation} \label{ref4}
\refstepcounter{equation} \label{ref5}

\obeylines % just for this example
\crefrange{ref1}{ref5}
\cref{ref1,ref5,ref4,ref3,ref2}      % arguments needn't be sorted
\labelcref{ref1,ref5,ref4,ref3,ref2} % ditto
\end{document}

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