At the interface between monolayer FeSe films and SrTiO3 substrates the superconducting transition temperature (Tc) is unexpectedly high, triggering a surge of excitement. The mechanism for the Tc enhancement has been the central question, as it may present a new strategy for seeking out higher Tc materials. To reveal this enigmatic mechanism, by combining advances in high quality interface growth, 16O [Formula: see text] 18O isotope substitution, and extensive data from angle resolved photoemission spectroscopy, we provide striking evidence that the high Tc in FeSe/SrTiO3 is the cooperative effect of the intrinsic pairing mechanism in the FeSe and interactions between the FeSe electrons and SrTiO3 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.