At the freezing point, why is the vapor pressure of the liquid phase equal to the vapor pressure of the solid phase? At the freezing point of a substance, the solid phase is in dynamic equilibrium with the liquid phase. My textbook defines the freezing point of a substance as: "the temperature at which the vapor pressure of the substance in its liquid phase is equal to its vapor pressure in the solid phase". Why is this so? How does the vapor phase even come into the picture during freezing? Shouldn't it be all about the solid and the liquid?

My book also states that when we add a non volatile solute to a liquid solvent, "the solution will freeze at the temperature when its vapor pressure is equal to the vapor pressure of the pure solid solvent". This doesn't make sense to me as well. Assuming the first statement is true, shouldn't the second statement read, "...is equal to the vapor pressure of the solid solution"? Are the two statements somehow related to each other?And why are they true?
If the vapor pressure of the substance in its liquid phase would be different from the vapor pressure of its solid phase then there would be a transfer of mass from the phase with the higher vapor pressure to the phase with the lower vapor pressure.

This would involve releasing or consuming energy (heat of fusion) even in a closed system in thermal equilibrium, which is obviously a contradiction.