如何将定义的命令改进为语句？

Question

首先，最小工作样本如下。

\documentclass{amsart}
\usepackage{tikz}

\makeatletter
\newcommand*\tikzdottedwedgesource{%
\tikz[baseline=-0.25em, line cap=round, dash pattern=on 0pt off 3\pgflinewidth]{%
\draw[line width=0.05375em] (0.00em,0.34em) -- (-0.204em,-0.288em);%
\draw[line width=0.05375em] (0.00em,0.34em) -- (0.204em,-0.288em);%
}}
\newcommand*\dottedwedgesource{\mathbin{\mkern1mu\tikzdottedwedgesource\mkern1mu}}

\newcommand*\macro@dottedbigwedge[2]{%
    \vcenter{\hbox{%
            \sbox\z@{$#1\bigwedge$}%
            \resizebox{!}{0.9\dimexpr\ht\z@+\dp\z@}{\raisebox{0\depth}{$\m@th#1\dottedwedgesource$}}%
    }}%
    \vphantom{\bigwedge}%
}
\newcommand*\dottedbigwedge{%
    \DOTSB\mathop{\mathpalette\macro@dottedbigwedge\relax}\slimits@%
}
\makeatother
\begin{document}
\[
\dottedbigwedge_x^y\phi=\bigwedge_x^y\phi.
\]
\end{document}

如你所见，我定义了一个大运算符\dashedbigwedge。我的问题是有没有什么办法可以让命令包含 no\bigwedge但又不改变命令的输出？。