At the interface between monolayer FeSe films and SrTiO substrates the superconducting transition temperature (T ) is unexpectedly high, triggering a surge of excitement. The mechanism for the T enhancement has been the central question, as it may present a new strategy for seeking out higher T materials. To reveal this enigmatic mechanism, by combining advances in high quality interface growth, O Formula: see text O isotope substitution, and extensive data from angle resolved photoemission spectroscopy, we provide striking evidence that the high T in FeSe/SrTiO is the cooperative effect of the intrinsic pairing mechanism in the FeSe and interactions between the FeSe electrons and SrTiO phonons. Furthermore, our results point to the promising prospect that similar cooperation between different Cooper pairing channels may be a general framework to understand and design high-temperature superconductors.