let R be Ring; :: thesis: for V being strict RightMod of R
for W being strict Submodule of V st ( for v being Vector of V holds v in W ) holds
W = V
let V be strict RightMod of R; :: thesis: for W being strict Submodule of V st ( for v being Vector of V holds v in W ) holds
W = V
let W be strict Submodule of V; :: thesis: ( ( for v being Vector of V holds v in W ) implies W = V )
assume for v being Vector of V holds v in W ; :: thesis: W = V
then A1: for v being Vector of V holds
( v in W iff v in V ) ;
V is Submodule of V by Th24;
hence W = V by A1, Th30; :: thesis: verum