Consider a constant volume system (a container) where vapor and liquid are at saturation temperature. If we cool down the system some of the vapor condenses. Will this bring down the pressure of the system or will it remain constant? What about the partial pressure of the vapor?
If the mixture is in Vapor-Liquid Equilibrium, then the saturation pressure drops together with the temperature. If you look in the saturation tables for different substances (Table A-4 in the attached link), you will observe this P-T dependence. The partial pressure of the vapor will also drop. You can also see this dependence if you are using the Antoine's equation (see link).
http://www.slideshare.net/chunfeichow5/appendix1-thermodynamics
https://en.wikipedia.org/wiki/Antoine_equation
Pressure will decrease with lowering temperature. If other gases are present, the partial pressure of the vapor decreases with temperature as per the saturation value.
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