Saturation dissolved oxygen level at pressure

The saturation level of dissolved oxygen in contact with a moist atmosphere is


$$c = 0.21(p\_\mathrm{atm} - p\_\mathrm{vap}) K\_\mathrm{H} M$$


where the $p\_\mathrm{atm}$ and $p\_\mathrm{vap}$ are the atmospheric and vapour pressures, respectively; $K\_\mathrm{H}$ is the Henry's law constant, and $M$ is the molar mass.


If I take this volume of water away from the atmospheric interface, and reduce the pressure, does the saturation level equation stay the same as above, except swapping out $p\_\mathrm{atm}$ for $p\_\mathrm{local}$?


