Le Chatelier's principle
If these reactions both occurred in the same reaction vessel, the solubility of the silver chloride would be increased by the presence of NH4OH because formation of the Diammine argentum(I) complex consumes a significant portion of the free silver ions from the solution. By Le Chatelier's principle, this causes the equilibrium reaction for the dissolving of the silver chloride, which has silver ion as a product, to shift to the right.