The intergenerational trade-off of the climate change issue is intuitive: the costs of reducing emissions today, borne by the present generation, represent an investment to avoid climate change damages, which would otherwise affect future generations. The relationship between intragenerational equity and our willingness to pay for mitigation is less straightforward, as it depends on present inequalities, expected future inequalities, as well as the effect of both mitigation and climate damages on those two. In this paper, we analyze the preferred emission reduction targets considering both inter and intragenerational equity for the wide range of socioeconomic projections of the Shared Socioeconomic Pathways. We show that accounting for intragenerational equity favors equally or more stringent emissions reductions targets than stand-alone intergenerational equity, suggesting that the distributional effects of impacts outweigh those of mitigation. We also find that the overall effect of inequality aversion depends on assumptions about economic convergence. We therefore argue that welfare analysis of climate mitigation cannot overlook the critical role of socioeconomic assumptions driving intragenerational inequalities.