A single-particle-propagator (i.e., Green's function) theory of evaporation from quantum liquids is developed and applied to the energy distribution of He3 atoms evaporating from He3-He4 mixtures. The resulting theoretical energy distribution contains no unknown parameters. We predict a distribution described in terms of an effective temperature which is somewhat higher than the temperature of the liquid. However, the effect is not so pronounced as the temperature shift observed by King and Johnston in the pure-He4 evaporation experiment. We suggest that experiments of this type might be used to measure the Bose condensate fraction of superfluid He4.