The trilepton nucleon decay modes p→e+νν and p→μ+νν violate |Δ(B-L)| by two units. Using data from a 273.4 kt yr exposure of Super-Kamiokande a search for these decays yields a fit consistent with no signal. Accordingly, lower limits on the partial lifetimes of τp→e+νν>1.7×10(32) years and τp→μ+νν>2.2×10(32) years at a 90% confidence level are obtained. These limits can constrain Grand Unified Theories which allow for such processes.