You can't, at least not directly. You could use a MultiBinding with all of the desired text boxes as inputs, but you will need to provide an IMultiValueConverter to "combine" the various text boxes into one object (such as a list):
<Button>
<Button.DataContext>
<MultiBinding Converter="{StaticResource ListMaker}">
<Binding ElementName="txtEmail" />
<Binding ElementName="txtFirstName" />
<Binding ElementName="txtLastName" />
</MultiBinding>
</Button.DataContext>
</Button>
And it is then that resulting list object that will be passed to your trigger, so you won't be able to access the Validation.HasError property directly: your DataTrigger will also need to bring in a converter which converts the list object into a boolean indicating whether Validation.HasError is set for anything in the list. At this point you might as well just forget about triggers and bind IsEnabled using a MultiBinding:
<Button>
<Button.IsEnabled>
<MultiBinding Converter="{StaticResource AllFalse}">
<Binding Path="(Validation.HasError)" ElementName="txtEmail" />
<Binding Path="(Validation.HasError)" ElementName="txtFirstName" />
<Binding Path="(Validation.HasError)" ElementName="txtLastName" />
</MultiBinding>
</Button.DataContext>
</Button>
(Here the AllFalse converter returns true if all inputs are false, and false if any input is true.)
A better approach, however, may be, instead of binding the Button directly to other UI elements, have your data object -- the same object that your text boxes are binding to -- expose an IsValid property (with suitable change notifications), and bind your Button.IsEnabled to that:
<Button IsEnabled="{Binding IsValid}" />
This moves you towards a MVVM-style solution which helps with things like testability (e.g. it's easy to create tests for the IsValid property; it's much harder to create tests for Button.IsEnabled).