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In this Letter we show that the evidence for neutrino oscillations from theSuper-Kamiokande atmospheric neutrino data fully determines the 3x3neutrino-oscillations mixing matrix and predicts an energy independent solarneutrino deficit at the level of 45%. This corresponds to a ratio of measuredto predicted neutrino flux of R_e^{Solar} = 0.55, in good agreement with theexperimental results. We achieve this result within the framework of a minimal,three-generations neutrino mixing, with mass squared differences of dM^2 = 0.45eV^2 and dm^2 = O(10^-3) eV^2. The mixing matrix derived here is characterizedby the mixing angles theta = 35.1, beta = 5.5, and psi = 23.3, and a vanishingCP-violating phase, delta = 0.Comment: LaTeX, 12 pages with 4 figures (EPS

CAN THE SUPER-KAMIOKANDE ATMOSPHERIC DATA PREDICT THE SOLAR NEUTRINO DEFICIT?