documentclass{article}
usepackage{amsmath}
usepackage{amsmath}
usepackage{adjustbox}

newcommand{veq}{mathrel{rotatebox{90}{$=$}}}
newcommand{vneq}{mathrel{rotatebox{90}{$neq$}}}

begin{document}

This is a test. Yes it is. Of course. Look here. Yes, Here. That's right. Mhmm. Words. Filler. Indeed. Look. A paragraph. With words. Here. Yes. And where's that? Where is here? It's right here:

[
left. frac{partial f(A,B,C,D)}{partial A} right|
raisebox{.9baselineskip}{$_{begin{array}{ccccc}
A & = & B & = & Z \
{} & {} & vneq & {} & {} \
C & neq & I & neq & W \
veq & {} & {} & {} & {} \
D & = & G & neq & Q^2+3 end{array} }$}
]

end{document}

documentclass{article}
usepackage{tabstackengine}
stackMath
makeatletter
renewcommandTAB@delim[1]{scriptstyle#1}
defreq{protectrotatebox{90}{$scriptstyle=$}}
defrne{protectrotatebox{90}{$scriptstylene$}}
makeatother
usepackage{graphicx}
begin{document}
[
setstackgap{L}{.6baselineskip}
left.frac{partial f(A,B,C,D)}{partial A}right|
raisebox{.9baselineskip}{$_{A = tabbedCenterstack{C\ req\0\ rne\ D} ne B}$}
]

[
setstackgap{L}{.6baselineskip}setstacktabulargap{0pt}TABbinary
left.frac{partial f(A,B,C,D)}{partial A}right|
raisebox{-.2baselineskip}%
{$_{tabularCenterstack{rcl}{A = & 0&\ &req&\&D& ne B = C}}$}
]

[
setstackgap{L}{.6baselineskip}setstacktabulargap{0pt}TABbinary
left.frac{partial f(A,B,C,D)}{partial A}right|
raisebox{.9baselineskip}%
{$_{tabularCenterstack{rcl}{L = & 0&\ &req&\A = &0& ne B = F\
  &rne&\ &D&ne B\&rne&\&E&}}$}
]
end{document}

documentclass{article}
usepackage{graphicx}
usepackage{mathtools}
usepackage{adjustbox}

newcommand{veq}{mathrel{rotatebox{90}{$=$}}}
newcommand{vneq}{mathrel{rotatebox{90}{$neq$}}}
newcommand*{VerticalRelations}[5]{%
    % #1 = center
    % #2 = above
    % #3 = symbol above
    % #4 = below
    % #5 = symbol below
    adjustbox{stack=cc}{%
        ensuremath{#2}\%
        ensuremath{mathclap{#3}}\%
        ensuremath{#1}\%
        ensuremath{#5}\%
        ensuremath{mathclap{#4}}%
    }%
}%
begin{document}
[
    A = VerticalRelations{0}{C}{veq}{D}{vneq} neq B
]
and check appropriate spacing for longer ``above" and ``below" text:
[
 A = VerticalRelations{0}{C}{veq}{Dneq B}{vneq} neq B
 ]
end{document}