Instead of importing the symbols from Computer Modern after loading mathabx, you can use \let to define aliases to the corresponding commands before to load the package. This way, you will still be able to use the symbols from Computer Modern with these aliases.
\documentclass{article}
\let\cmin\in
\let\cmsubset\subset
\let\cmsupset\supset
\let\cmcap\cap
\let\cmcup\cup
\let\cmland\land
\let\cmlor\lor
\let\cmLeftarrow\Leftarrow
\let\cmRightarrow\Rightarrow
\let\cmLeftrightarrow\Leftrightarrow
\usepackage{mathabx}
\begin{document}
\( \in\subset\supset\cap\cup\land\lor\Leftarrow\Rightarrow\Leftrightarrow \)
( \cmin\cmsubset\cmsupset\cmcap\cmcup\cmland\cmlor\cmLeftarrow\cmRightarrow\cmLeftrightarrow )
\end{document}

If you want, you can of course renew all of these commands so that the usual commands refer to the symbols from Computer Modern rather than those of mathabx.
\documentclass{article}
\let\cmin\in
\let\cmsubset\subset
\let\cmsupset\supset
\let\cmcap\cap
\let\cmcup\cup
\let\cmland\land
\let\cmlor\lor
\let\cmLeftarrow\Leftarrow
\let\cmRightarrow\Rightarrow
\let\cmLeftrightarrow\Leftrightarrow
\usepackage{mathabx}
\let\in\cmin
\let\subset\cmsubset
\let\supset\cmsupset
\let\cap\cmcap
\let\cup\cmcup
\let\land\cmland
\let\lor\cmlor
\let\Leftarrow\cmLeftarrow
\let\Rightarrow\cmRightarrow
\let\Leftrightarrow\cmLeftrightarrow
\begin{document}
\( \in\subset\supset\cap\cup\land\lor\Leftarrow\Rightarrow\Leftrightarrow \)
\end{document}
