The table is not centering in the item

A MWS is as following.

\documentclass{article}

\renewcommand{\labelenumi}{(\theenumi)}
\usepackage{enumitem}
\setenumerate[1,2,3]{itemsep=0pt,partopsep=0.3\baselineskip plus 0.2ex minus 0.1ex,parsep=0pt,topsep=0pt}
\setitemize[1,2,3]{itemsep=0pt,partopsep=0.3\baselineskip plus 0.2ex minus 0.1ex,parsep=0pt,topsep=0pt,align=left}
\setdescription[1,2,3]{itemsep=0pt,partopsep=0.3\baselineskip plus 0.2ex minus 0.1ex,parsep=0pt,topsep=0pt,align=left}
\setlist[enumerate]{leftmargin=2em,align=left,labelwidth=2em,labelsep=0em}%\parindent=2em
\setlist[itemize]{leftmargin=1em,align=left,labelwidth=1em,labelsep=0em}
\setlist[description]{leftmargin=2em,align=left,labelwidth=1em,labelsep=1em}

\usepackage{amsthm}
\theoremstyle{theorem}
\newtheorem{theorem}{Theorem}[section]
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{remark}[theorem]{Remark}

\usepackage{longtable, makecell, booktabs, multicol, multirow}
\usepackage{lipsum}

\begin{document}
\section{Test}

\begin{remark}
\begin{enumerate}
\item \lipsum[1]
\begingroup
%\setlength{\LTleft}{0pt}\setlength{\LTright}{0pt} 
\begin{longtable}{p{1cm}<{\centering}p{1cm}<{\centering}p{1.5cm}<{\centering}p{1.5cm}<{\centering}p{2.5cm}<{\centering}}
\caption{On Implications}
\\\toprule
$\phi$&$\psi$&$\phi\to\psi$&$\phi\wedge\psi$&$\phi\wedge\psi\to\phi$\\
\midrule\endfirsthead%
\midrule
$\phi$&$\psi$&$\phi\to\psi$&$\phi\wedge\psi$&$\phi\wedge\psi\to\phi$\\
\midrule\endhead
\midrule\endfoot
\bottomrule\endlastfoot
1&1&1&1&1\\
1&0&0&0&1\\
0&1&$x$&0&1\\
0&0&$y$&0&1\\
\end{longtable}
\endgroup
\lipsum[2]
\item \lipsum[3]
\end{enumerate}
\end{remark}

\end{document}

As you see, the table is centering on the page in in horizontal direction but not centering in the item of the enumerate environment. Is there any way to make the table be centering in the item of the enumerate environment?