Latex: Left alignment for an equation - latex

Question

I have these two definitions:
\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
\begin{flalign*}
&\boldsymbol{R*^\sigma} & \sigma_{superset}(F)&=\sigma_{superset}(F')&\\
&\boldsymbol{R*_{weak}^\sigma} & \sigma_{superset}(F)&=\sigma_{superset}(F')\cap\mathcal{P}(A)&
\end{flalign*}
\end{document}
Compiled, it looks like this:
I want the equations to be aligned by "=" as they are; but also that they are not centered but quite next to the bold symbols. Like, also aligned left.
It should look like this (done with MS Paint):

Answer 1

If you don't mind that all equations will be left aligned, you could use the fleqn option of amsmath:
\documentclass[12pt]{article}
\usepackage[fleqn]{amsmath}
\setlength{\mathindent}{0pt}
\begin{document}
\noindent text
\begin{alignat*}{3}
&\boldsymbol{R*^\sigma} & \sigma_{superset}(F)&=\sigma_{superset}(F')\\
&\boldsymbol{R*_{weak}^\sigma} \quad& \sigma_{superset}(F)&=\sigma_{superset}(F')\cap\mathcal{P}(A)
\end{alignat*}
\end{document}
If you like to keep other equations centred, you could also switch temporarily:
\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
\[
a
\]
{
\makeatletter
\#fleqntrue
\makeatother
\begin{alignat*}{4}
&\boldsymbol{R*^\sigma} & \sigma_{superset}(F)&=\sigma_{superset}(F')\\
&\boldsymbol{R*_{weak}^\sigma} \quad& \sigma_{superset}(F)&=\sigma_{superset}(F')\cap\mathcal{P}(A)
\end{alignat*}
}
\[
a
\]
\end{document}