As a result of global efforts to reduce greenhouse gas emissions, future energy system designs must be investigated. However, previous studies in integrated generation and transmission expansion planning neglect indirect emissions and therefore the full global warming potential of system designs. We introduce a linear, single-stage integrated expansion planning model with respect to global warming potential of all components. Neglecting indirect emissions underestimates the global warming potential by more than 20% and the total cost by almost 10% in an exemplary showcase. The inclusion of indirect emissions tightens the emission budget and therefore leads to different system designs.