The AMS symbol fonts don't provide bold versions and neither do the mathabx fonts.
You can use the symbols in MnSymbol, but they're smaller than the CM fonts; scaling them will thicken their strokes. Here's an experiment:
\documentclass{article}
\usepackage{amssymb,bm}
\DeclareFontFamily{U}{MnSymbolD}{}
\DeclareFontShape{U}{MnSymbolD}{m}{n}{
<-6> s*[1.2] MnSymbolD5
<6-7> s*[1.2] MnSymbolD6
<7-8> s*[1.2] MnSymbolD7
<8-9> s*[1.2] MnSymbolD8
<9-10> s*[1.2] MnSymbolD9
<10-12> s*[1.2] MnSymbolD10
<12-> s*[1.2] MnSymbolD12}{}
\DeclareFontShape{U}{MnSymbolD}{b}{n}{
<-6> s*[1.2] MnSymbolD-Bold5
<6-7> s*[1.2] MnSymbolD-Bold6
<7-8> s*[1.2] MnSymbolD-Bold7
<8-9> s*[1.2] MnSymbolD-Bold8
<9-10> s*[1.2] MnSymbolD-Bold9
<10-12> s*[1.2] MnSymbolD-Bold10
<12-> s*[1.2] MnSymbolD-Bold12}{}
\DeclareSymbolFont{MnSyD}{U}{MnSymbolD}{m}{n}
\SetSymbolFont{MnSyD}{bold}{U}{MnSymbolD}{b}{n}
\DeclareMathSymbol\prec{\mathrel}{MnSyD}{"68}
\DeclareMathSymbol\succ{\mathrel}{MnSyD}{"69}
\DeclareMathSymbol\preceq{\mathrel}{MnSyD}{"6A}
\DeclareMathSymbol\succeq{\mathrel}{MnSyD}{"6B}
\DeclareMathSymbol\preccurlyeq{\mathrel}{MnSyD}{"6C}
\DeclareMathSymbol\succcurlyeq{\mathrel}{MnSyD}{"6D}
\DeclareMathSymbol\precsim{\mathrel}{MnSyD}{"6E}
\DeclareMathSymbol\succsim{\mathrel}{MnSyD}{"6F}
\DeclareMathSymbol\precapprox{\mathrel}{MnSyD}{"70}
\DeclareMathSymbol\succapprox{\mathrel}{MnSyD}{"71}
\begin{document}
$\prec\succ\preceq\succeq\preccurlyeq\succcurlyeq\precsim\succsim$
$<>$
\mathversion{bold}
$\prec\succ\preceq\succeq\preccurlyeq\succcurlyeq\precsim\succsim$
$<>$
\end{document}

At natural size (with [1.0] or removing s*[1.2] altogether)

With also negated symbols (at natural size)
\documentclass{article}
\usepackage{amssymb,bm}
\DeclareFontFamily{U}{MnSymbolD}{}
\DeclareFontShape{U}{MnSymbolD}{m}{n}{
<-6> MnSymbolD5
<6-7> MnSymbolD6
<7-8> MnSymbolD7
<8-9> MnSymbolD8
<9-10> MnSymbolD9
<10-12> MnSymbolD10
<12-> MnSymbolD12}{}
\DeclareFontShape{U}{MnSymbolD}{b}{n}{
<-6> MnSymbolD-Bold5
<6-7> MnSymbolD-Bold6
<7-8> MnSymbolD-Bold7
<8-9> MnSymbolD-Bold8
<9-10> MnSymbolD-Bold9
<10-12> MnSymbolD-Bold10
<12-> MnSymbolD-Bold12}{}
\DeclareSymbolFont{MnSyD}{U}{MnSymbolD}{m}{n}
\SetSymbolFont{MnSyD}{bold}{U}{MnSymbolD}{b}{n}
\DeclareMathSymbol\prec{\mathrel}{MnSyD}{"68}
\DeclareMathSymbol\succ{\mathrel}{MnSyD}{"69}
\DeclareMathSymbol\preceq{\mathrel}{MnSyD}{"6A}
\DeclareMathSymbol\succeq{\mathrel}{MnSyD}{"6B}
\DeclareMathSymbol\preccurlyeq{\mathrel}{MnSyD}{"6C}
\DeclareMathSymbol\succcurlyeq{\mathrel}{MnSyD}{"6D}
\DeclareMathSymbol\precsim{\mathrel}{MnSyD}{"6E}
\DeclareMathSymbol\succsim{\mathrel}{MnSyD}{"6F}
\DeclareMathSymbol\precapprox{\mathrel}{MnSyD}{"70}
\DeclareMathSymbol\succapprox{\mathrel}{MnSyD}{"71}
\DeclareMathSymbol\nprec{\mathrel}{MnSyD}{"E0}
\DeclareMathSymbol\nsucc{\mathrel}{MnSyD}{"E1}
\DeclareMathSymbol\npreceq{\mathrel}{MnSyD}{"E2}
\DeclareMathSymbol\nsucceq{\mathrel}{MnSyD}{"E3}
\DeclareMathSymbol\npreccurlyeq{\mathrel}{MnSyD}{"E4}
\DeclareMathSymbol\nsucccurlyeq{\mathrel}{MnSyD}{"E5}
\DeclareMathSymbol\nprecsim{\mathrel}{MnSyD}{"E6}
\DeclareMathSymbol\nsuccsim{\mathrel}{MnSyD}{"E7}
\DeclareMathSymbol\nprecapprox{\mathrel}{MnSyD}{"E8}
\DeclareMathSymbol\nsuccapprox{\mathrel}{MnSyD}{"E9}
\begin{document}
$\prec\succ\preceq\succeq\preccurlyeq\succcurlyeq\precsim\succsim$
$<>$
$\nprec\nsucc\npreceq\nsucceq\npreccurlyeq\nsucccurlyeq\nprecsim\nsuccsim$
\mathversion{bold}
$\prec\succ\preceq\succeq\preccurlyeq\succcurlyeq\precsim\succsim$
$<>$
$\nprec\nsucc\npreceq\nsucceq\npreccurlyeq\nsucccurlyeq\nprecsim\nsuccsim$
\end{document}

MnSymbolhas a bold version. You might import only the bold version of this character. – Bernard Dec 24 '17 at 15:48mathabxversion is mostly compatible with CM, other symbol fonts have quite different symbols. – egreg Dec 24 '17 at 17:32mathabxhas a bold version. – Bernard Dec 24 '17 at 17:53