My I ask which anti ice valve? Engine or wing?
Other people may have different experiences, but for mine I have never been able to get a tech crew agree to dispatch with the anti ice inop in the closed position and to be honest I have only ever offered the MEL to see the reaction. ( I have often wondered why we have the MEL available to us as I am yet to see a practical use)
The reason, weather being the fickle thing that it is, no one is willing to guarantee the weather conditions at the destination to risk dispatch into icing conditions without protection..
Just to clarify, I have no experience on the 777 , only many other Boeings and Airbii