The various phases observed in all cuprate superconductors [superconducting (SC), spin-glass (SG), and antiferromagnetic (AFM)] were investigated with respect to oxygen-isotope (16O/18O) effects, using here as a prototype system of cuprates Y1-xPrxBa2Cu3O7-delta. All phases exhibit an isotope effect which is strongest where the respective phase terminates. In addition, the isotope effects on the magnetic phases (SG and AFM) are sign reversed as compared to the one on the superconducting phase. In the coexistence regime of the SG and SC phase a two-component behavior is observed where the isotope induced decrease of the superfluid density leads to a corresponding enhancement in the SG related density.