Using def inside mathematical environment

I have the following:

documentclass{article}

usepackage{amsmath}
usepackage{witharrows}


begin{document}
    
defvar{x}
    
[
    begin{WithArrows}
        varvar&=defvar{y}varvar\
        var
    end{WithArrows}
]

end{document}

I wanted to change the var value to y but it only works for the var immediatly after the def and on that line.

The result of the compilation is:

And I’m wondering why the var on the second line is not affected by the instruction above.

documentclass{article}

usepackage{amsmath}
usepackage{witharrows}


begin{document}
    
defvar{x}
    
[
    begin{WithArrows}
        varvar&=gdefvar{y}varvar\
        var
    end{WithArrows}
]

end{document}