The Trojan horse nucleus invariance for the binary reaction cross section extracted from the Trojan horse reaction was tested using the quasifree 3He(6Li,αα)H and 3He(7Li,αα)2H reactions. The cross sections for the 6Li(d,α)4He and 7Li(p,α)4He binary processes were extracted in the framework of the plane wave approximation. They are compared with direct behaviors as well as with cross sections extracted from previous indirect investigations of the same binary reactions using deuteron as the Trojan horse nucleus instead of 3He. The very good agreement confirms the applicability of the plane wave approximation which suggests the independence of the binary indirect cross section on the chosen Trojan horse nucleus, at least for the investigated cases.