Quantifier is too small next to dfrac

Question

I want to work with fractions, quantifying a fraction as single element, but \forall and \exists are being displayed too small near \dfrac. And mathlarger doesn't seem to work.

I know only the basics of latex and haven't found anything that resolves this problem.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{relsize}

\begin{document}
    \begin{enumerate}
        \item Neutral: $\mathlarger{\exists!} \dfrac{x}{y} : \dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}$
    \end{enumerate}
\end{document}

Answer 1

Perhaps what you need is a symbol which acts like a large operator. See the following codes and output.

\documentclass{article}
\usepackage{amsmath}
\usepackage{scalerel}
\makeatletter
\DeclareMathOperator*{\bigexistsone}{\scalerel*{\exists!}{\sum}}
\makeatother

\begin{document}
\begin{enumerate}
\item The original one in text style in lines: $\exists!\dfrac{x}{y}\left(\dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}\right)$, and the new one in display style between lines: $$\exists!\dfrac{x}{y}\left(\dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}\right).$$
\item The new one in text style in lines: $\bigexistsone\dfrac{x}{y}\left(\dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}\right)$, and the new one in display style between lines: $$\bigexistsone\dfrac{x}{y} \left(\dfrac{x}{y} + \dfrac{c}{d} = \dfrac{c}{d}\right).$$
\end{enumerate}

\end{document}