\documentclass{article}

\usepackage[latin2]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[magyar]{babel}

\begin{document}

$\{\,x\mid P_x\,\}$, $2\mid n$, $f\big|_H$
$\left| \left|x\right|^3 - 
        \left|y\right| \right|$

\end{document}