The Trojan horse nucleus invariance for the binary d(d,p)t reaction was tested by means of an experiment using the quasifree 2H(6Li,pt)4He and 2H(3He,pt)H reactions after 6Li and 3He breakup, respectively. The astrophysical S(E) factor for the d(d,p)t binary process was extracted from the present data in the framework of the plane wave approximation applied to the two different breakup schemes. The obtained results are compared with direct data as well as with previous indirect investigations. The very good agreement confirms the applicability of the plane wave approximation and suggests the independence of the binary indirect cross section on the chosen Trojan horse nucleus also for the present case.