A system and method for cryogenic purification of a hydrogen, nitrogen, methane and argon containing feed stream to produce a methane free, hydrogen and nitrogen containing synthesis gas and a methane rich fuel gas, as well as to recover an argon product stream, excess hydrogen, and excess nitrogen is provided. The disclosed system and method are particularly useful as an integrated cryogenic purifier in an ammonia synthesis process in an ammonia plant. The excess nitrogen is a nitrogen stream substantially free of methane and hydrogen that can be used in other parts of the plant, recovered as a gaseous nitrogen product and/or liquefied to produce a liquid nitrogen product.