# Attempting to mimic the spacing from another line using \phantom and \mathrel doesn't work

Here is an example document.

\documentclass{amsart}

\begin{document}

We define two more $B$--symbols, $\zeta_1$ and $\zeta_2$, as follows: for each $x_J \in M(B)$ and each $j \in J$, $\zeta_1(B, J, j)$ and $\zeta_2(B, J, j)$ are integers given by:
\begin{align*}
\zeta_1(B, J, j) \; &:= \phantom{2} \mathrel{\phantom{\times}} |\{b \in B : b > j\}|
\\ \zeta_2(B, J, j) \; &:= 2 \times |\{b \in J : b > j\}|.
\end{align*}
We define the $B$--symbol $\zeta$ as follows: for each $x_J \in M(B)$ and each $j \in J$, $\zeta(B, J, j)$ is given by $\zeta_1(B, J, j) - \zeta_2(B, J, j)$.

\end{document}

Here is a close-up of the output:

The relevant code used to attempt to add the correct amount of extra spacing is this bit:

\phantom{2} \mathrel{\phantom{\times}}

But this isn't spaced correctly. It produces slightly too much spacing, as you can see from the picture. How come?

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