We know that the Gorenstein projectivity relative to a semidualizing module is preserved under excellent extensions. A new method of proof is adopted when the conclusion is known to be correct. Using the equivalent proposition of the definition to prove that for an excellent extension R→S and an S-module SM,RMisGCprojective module if and only ifSM isGSRCprojective module. The form of the new method after using equivalent proposition is uniform. It is convenient to generalize and apply the related properties of modules.