let R be Ring; :: thesis: for V being RightMod of R holds V is Submodule of V
let V be RightMod of R; :: thesis: V is Submodule of V
A1: the rmult of V = the rmult of V | [: the carrier of V, the carrier of R:] by RELSET_1:19;
( 0. V = 0. V & the addF of V = the addF of V | [: the carrier of V, the carrier of V:] ) by RELSET_1:19;
hence V is Submodule of V by A1, Def2; :: thesis: verum