Spacing between two relational symbols

Question

I have a relation symbol that I want to define through an equality. The problem is that when I do this, LaTeX puts too little space between the relation symbol and the equality symbol. My guess is that this is because both are relation symbols. Here is a MWE:

\documentclass{article}
\begin{document}
  \[\cong_{\mathcal{F}} = \{(x,y) \in X^2 \mid \forall F \in \mathcal{F}. x \in F \iff y \in F\}.\]
\end{document}

If I specify that = should be a binary operator, then the spacing between those two symbols is correct, but now the spacing between equality and the following set is too small:

\documentclass{article}
\begin{document}
  \[\cong_{\mathcal{F}} \mathbin{=} \{(x,y) \in X^2 \mid \forall F \in \mathcal{F}. x \in F \iff y \in F\}.\]
\end{document}

So my question is: How do I ensure that the spacing around = is correct on both sides? I could try hacking it by inserting spacing manually until I'm happy, but I am hoping for a more standardised answer that will also work in other situations.

Answer 1

Just brace the symbol:

\documentclass{article}
\begin{document}

\[
{\cong_{\mathcal{F}}} = \{(x,y) \in X^2 \mid \forall F \in \mathcal{F}. x \in F \iff y \in F\}.  
\]

\end{document}

What happens is that TeX adds no space between consecutive relation atoms (\cong_{\mathcal{F}} and =), but when a symbol is braced it becomes an “ordinary atom”, just like a letter.