Hide / Show DataGridColumn with ContextMenu

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XAML

WPF

MVVM

C#5.0

Hello everybody,

I've got a DataGrid with a number of columns, which I've manually defined in xaml.

<DataGrid ItemsSource="{Binding SearchResult}" AutoGenerateColumns="False">
       <DataGridTextColumn Header="Column1" Binding="{Binding Property1}" />
       <DataGridTextColumn Header="Column2" Binding="{Binding Property2}" />
        ...
</DataGrid>

Now I'd like to have a ContextMenu in which each column has a MenuItem with checkbox to hide or show the Column.

<ConextMenu ItemSource="{Binding Columns}">
   <MenuItem>
      <MenuItem.Icon><CheckBox IsChecked="{Binding IsVisible}" /></MenuItem.Icon>
      <MenuItem.Header><TextBlock Text="{Binding ColumnHeader}" /></MenuItem.Header>
   </MenuItem>
   ....
</ContextMenu>

How can I implement this with Bindings?

Thanks a lot for your reply.