Equivalent local martingale measures exclude admissible arbitrage

Suppose a finite-horizon market has a strictly positive numéraire $B$ and an equivalent measure under which all prices $S^i/B$ are local martingales. The discounted wealth of a self-financing strategy is a stochastic integral against those prices. If it is bounded below by a deterministic constant, that wealth is a supermartingale: add the lower-bound constant to obtain a nonnegative local martingale, then apply conditional Fatou to a localizing sequence. A zero-cost admissible portfolio therefore has expected discounted terminal wealth at most zero. Nonnegative terminal wealth with positive probability of a strict gain would have strictly positive expectation under the equivalent measure, a contradiction. Thus there is no admissible arbitrage. True martingales are not needed for this implication.