Our paper integrates results from trade-in-task theory into mainstream trade theory by developing trade-in-task analogues to the four famous theorems (Heckscher-Ohlin, factor price equalisation, Stolper-Samuelson, and Rybczynski) and showing the standard gains-from-trade theorem does not hold for trade-in-tasks. We show trade-in-tasks creates intraindustry trade in a Walrasian economy, and derive necessary and sufficient conditions for analyzing the impact of trade-in-tasks on wages and production. Extensions of the integrating framework easily accommodate monopolistic competition and two-way offshoring/trade-in-tasks.