amsmath: combine \nonumber and \label

Question

I'd like to write something as

\begin{align}
f(x) & = x + 1 \nonumber \\
& =: \eqref{eq:foo} \label{eq:foo} \nonumber \\
g(x) & = x + 2 \nonumber \\
& =: \eqref{eq:bar} \label{eq:bar} \nonumber
\end{align}

but amsmath does not allow me to do it:

! Package amsmath Error: Multiple \label's: label 'eq:foo' will be lost.See the amsmath package documentation for explanation.Type H for immediate help....

So what shall I do to solve this problem?

Interestingly

\begin{align}
f(x) & = x + 1 \nonumber \\
& =: \eqref{eq:foo} \label{eq:foo} \nonumber
\end{align}

is accepted by LaTeX, but the reference always stays a (??), even if I run LaTeX multiple times.

Answer 1

I find doing this quite disputable. Anyway, here it is:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\let\latexlabel\ltx@label
\makeatother
\newcommand{\assignnumber}[1]{%
  \refstepcounter{equation}\latexlabel{#1}\eqref{#1}%
}

\begin{document}
Here's a normal equation
\begin{equation}
0=0
\end{equation}
and now the thing you want
\begin{align*}
f(x) & = x + 1 \\
& =: \assignnumber{eq:foo} \\
g(x) & = x + 2  \\
& =: \assignnumber{eq:bar}
\end{align*}
with another equation to check the assigned numbers are correct
\begin{equation}
1=1
\end{equation}
with references to \eqref{eq:foo} and \eqref{eq:bar}.

\end{document}

The bulk is to override the amsmath way of assigning numbers and labels.