let x be object ; :: thesis: for R being Ring
for V being RightMod of R
for W being Submodule of V st x in W holds
x in V
let R be Ring; :: thesis: for V being RightMod of R
for W being Submodule of V st x in W holds
x in V
let V be RightMod of R; :: thesis: for W being Submodule of V st x in W holds
x in V
let W be Submodule of V; :: thesis: ( x in W implies x in V )
assume x in W ; :: thesis: x in V
then A1: x in the carrier of W ;
the carrier of W c= the carrier of V by Def2;
hence x in V by A1; :: thesis: verum