We prove a theorem on the existence of general equilibrium for a production economy with unordered preferences in a topological vector lattice commodity space. Our consumption sets need not have a lower bound and the set of feasible allocations need not be topologically bounded. Instead, we introduce a notion of local proper dominance and assume that the set of feasible allocations not locally properly dominated by any other feasible allocation has compact closure. Furthermore, we assume that the economy is locally proper as opposed to uniformly proper. In particular, preferences satisfy a locally uniform version of the extreme desirability condition of Yannelis and Zame [Yannelis, N.C., Zame, W.R., 1986, Equilibria in Banach lattices without ordered preferences, Journal of Mathematical Economics 15, 85–110.].