datatrigger cannot set bound property - wpf

Question

I have 2 checkboxes (chkMfsUi and chkMfs). When I check chkMfsUi, I also want to check chkMfs (and disable it).
I tried it with a datatrigger:
<Style x:Key="MfsCheckBoxStyle" TargetType="CheckBox">
<Setter Property="IsEnabled" Value="True" />
<Setter Property="IsChecked" Value="False" />
<Style.Triggers>
<DataTrigger Binding="{Binding IsChecked, ElementName=chkMfsUi}" Value="True">
<Setter Property="IsEnabled" Value="False" />
<Setter Property="IsChecked" Value="True" />
</DataTrigger>
</Style.Triggers>
</Style>
And these are my checkboxes:
<StackPanel>
<CheckBox Name="chkMfsUi"
Checked="CheckBox_Checked"
Content="MFS - UI"
IsChecked="{Binding MfsUi}"
Unchecked="CheckBox_Checked" />
<CheckBox Content="MFS" IsChecked="{Binding Mfs}" Style="{StaticResource MfsCheckBoxStyle}" />
</StackPanel>
The IsEnabled property work fine, but the IsChecked doesn't. Maybe because it is bound? I am also using INotifyPropertyChanged with these properties.
If I set it in code behind, it works, but is it possible with a trigger though?
Regards,
Alfons
EDIT:
As appeared from the current answers, my question seems to be incomplete. I need to have the following three states:
AND last but not least: Both checkboxes' IsChecked properties must be bound! (This is the moment when the trouble comes in)

Answer 1

Try this
<StackPanel Grid.Column="1">
<CheckBox x:Name="chkMfsUi" IsChecked="True"></CheckBox>
<CheckBox x:Name="chkMfs" IsChecked="{Binding ElementName=chkMfsUi,Path=IsChecked}">
<CheckBox.Style>
<Style TargetType="CheckBox">
<Style.Triggers>
<Trigger Property="IsChecked" Value="True">
<Setter Property="IsEnabled" Value="False"/>
</Trigger>
</Style.Triggers>
</Style>
</CheckBox.Style>
</CheckBox>
Another Method : By using style in resource
Add this namespace first xmlns:Globalvaribale="clr-namespace:System;assembly=mscorlib"
<Window x:Class="WpfApplication2.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:Globalvaribale="clr-namespace:System;assembly=mscorlib">
<Window.Resources>
<Globalvaribale:String x:Key="chkMfsUi">chkMfsUi</Globalvaribale:String>
<Style x:Key="chkMfsstyle" TargetType="CheckBox">
<Style.Triggers>
<DataTrigger Binding="{Binding IsChecked,ElementName={StaticResource chkMfsUi}}" Value="True">
<Setter Property="IsEnabled" Value="False"/>
<Setter Property="IsChecked" Value="True"/>
</DataTrigger>
</Style.Triggers>
</Style>
</Window.Resources>
<StackPanel Grid.Column="1">
<CheckBox x:Name="chkMfsUi"></CheckBox>
<CheckBox Style="{StaticResource chkMfsstyle}"/>
</StackPanel>
Output

Answer 2

In this case you can use the EventTrigger:
Represents a trigger that applies a set of actions in response to an event.
Example:
<StackPanel>
<StackPanel.Triggers>
<EventTrigger RoutedEvent="CheckBox.Checked" SourceName="First">
<BeginStoryboard>
<Storyboard>
<BooleanAnimationUsingKeyFrames Storyboard.TargetName="Second"
Storyboard.TargetProperty="IsChecked">
<DiscreteBooleanKeyFrame KeyTime="00:00:00" Value="True" />
</BooleanAnimationUsingKeyFrames>
</Storyboard>
</BeginStoryboard>
</EventTrigger>
<EventTrigger RoutedEvent="CheckBox.Checked" SourceName="Second">
<BeginStoryboard>
<Storyboard>
<BooleanAnimationUsingKeyFrames Storyboard.TargetName="First"
Storyboard.TargetProperty="IsChecked">
<DiscreteBooleanKeyFrame KeyTime="00:00:00" Value="True" />
</BooleanAnimationUsingKeyFrames>
</Storyboard>
</BeginStoryboard>
</EventTrigger>
<EventTrigger RoutedEvent="CheckBox.Unchecked" SourceName="First">
<BeginStoryboard>
<Storyboard>
<BooleanAnimationUsingKeyFrames Storyboard.TargetName="Second"
Storyboard.TargetProperty="IsChecked">
<DiscreteBooleanKeyFrame KeyTime="00:00:00" Value="False" />
</BooleanAnimationUsingKeyFrames>
</Storyboard>
</BeginStoryboard>
</EventTrigger>
<EventTrigger RoutedEvent="CheckBox.Unchecked" SourceName="Second">
<BeginStoryboard>
<Storyboard>
<BooleanAnimationUsingKeyFrames Storyboard.TargetName="First"
Storyboard.TargetProperty="IsChecked">
<DiscreteBooleanKeyFrame KeyTime="00:00:00" Value="False" />
</BooleanAnimationUsingKeyFrames>
</Storyboard>
</BeginStoryboard>
</EventTrigger>
</StackPanel.Triggers>
<CheckBox Name="First"
Content="First" />
<CheckBox Name="Second"
Content="Second" />
</StackPanel>
The Storyboard can be stored in Resources for readability, like so:
<Window.Resources>
<Storyboard x:Key="FirstCheckedStory" ... />
</Window.Resources>
And then use like this:
<EventTrigger RoutedEvent="CheckBox.Checked" SourceName="First">
<BeginStoryboard Storyboard="{StaticResource FirstCheckedStory}" />
</EventTrigger>
Also, the Storyboard can contain several actions, just put him in order:
<Storyboard>
<BooleanAnimationUsingKeyFrames ... />
<BooleanAnimationUsingKeyFrames ... />
</Storyboard>