Synchronous bursts of high frequency oscillations ("ripples") are hypothesized to contribute to binding by facilitating integration of neuronal firing across cortical locations. We tested this hypothesis using local field-potentials and single-unit firing from four 96-channel microelectrode arrays in supragranular cortex of 3 patients. Neurons in co-rippling locations showed increased short-latency co-firing, prediction of each-other's firing, and co-participation in neural assemblies. Effects were similar for putative pyramidal and interneurons, during NREM sleep and waking, in temporal and Rolandic cortices, and at distances up to 16mm. Increased co-prediction during co-ripples was maintained when firing-rate changes were equated, and were strongly modulated by ripple phase. Co-ripple enhanced prediction is reciprocal, synergistic with local upstates, and enhanced when multiple sites co-ripple. Together, these results support the hypothesis that trans-cortical co-ripples increase the integration of neuronal firing of neurons in different cortical locations, and do so in part through phase-modulation.