Enthalpy of the Universe

[ahyaa]

My professor posed a theoretical question today and I can't seem to figure this out. The prompt was this:

Calculate the enthalpy change of water ΔH when 18 grams of water ice at 230 K are converted to liquid water at 350 K. Also calculate the enthalpy change of the heating block as a result of this process and the enthalpy change of the universe as a result of this process.

I don't have a problem with the calculation of the enthalpy change of water etc., what I can't seem to figure out is how to prove that the enthalpy change of the universe will be zero. I was curious if anyone has been able to prove this? The best I got was ΔH_surr + ΔH_sys = ΔHuniv = 0 because ΔH_surr = -ΔH_sys.