Total Pressure of 2-Phase System: Dalton's Partial Pressure Law

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Sum of Partial Pressures of Gas phase equals to total pressure of a 2 phase system? It sounds illogical because in a 2 phase system, the liquid phase also exerts pressure as well. Under dalton's partial pressure law, it states that the sum of total partial pressures of each gas component is equals to the total pressure of the gas.

y(i) Ptotal + y(j) Ptotal =Ptotal

If this law is applicable even to a 2 phase system, wouldn't it be inaccurate to not account for the pressure of the liquid phase also?
 
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Dalton's law describes behavior of gases.
 
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So as to state, if I have a closed container at 1 atm that has 2 component 2 phases of liquid air, liquid water and gaseous air, gaseous water, the partial pressure of gaseous water is then y(H20) x Ptotal whereby Ptotal = 1 atm. Since we are using Ptotal in the calculations, would we ignore the hydrostatic pressure caused by the liquid form as well?
 


Hydrostatic pressure means that pressure on the bottom of the container differs from the pressure on the liquid surface. Whether you take it into account or not depends on what pressure you are calculating - it is not constant inside.