let R be Ring; :: thesis: for V being strict RightMod of R
for W being strict Submodule of V st the carrier of W = the carrier of V holds
W = V
let V be strict RightMod of R; :: thesis: for W being strict Submodule of V st the carrier of W = the carrier of V holds
W = V
let W be strict Submodule of V; :: thesis: ( the carrier of W = the carrier of V implies W = V )
assume A1: the carrier of W = the carrier of V ; :: thesis: W = V
V is Submodule of V by Th24;
hence W = V by A1, Th29; :: thesis: verum