You can't do that with dcases, as far as I know, but there are two ways to obtain what you want:
- either use the
empheq package and an alignat environment (possibly with `subequations, depending on how you want to number the cases),
- or use the
numcases or the subnumcases environment from the cases package.
Here are codes for each:
\documentclass[12pt, a4paper]{article}
\usepackage{amsthm, amssymb, mathrsfs}
\usepackage{empheq}
\usepackage{cases}
\begin{document}
\begin{numcases}{f(x) =}
1 & $ x \geq 0 $\label{pos} \\
0 & $ x < 0 $ \label{neg}
\end{numcases}
\begin{subnumcases}{f(x) =}
1 & $ x \geq 0 $\label{P} \\
0 & $ x < 0 $ \label{N}
\end{subnumcases}
\begin{empheq}[left={f(x) = \empheqlbrace\,}]{alignat=2}
1&\quad x\geq0\label{positive}\\
0&\quad x<0\label{negative}
\end{empheq}
\begin{subequations}
\begin{empheq}[left={f(x) = \empheqlbrace\,}]{alignat=2}
1&\quad x\geq0\label{Positive}\\
0&\quad x<0\label{Negative}
\end{empheq}
\end{subequations}
So by \eqref{positive}, \eqref{Positive},\eqref{P} and\eqref{pos}, we have %…
\end{document}
