let R be Ring; :: thesis: for V being RightMod of R
for W1, W2 being strict Submodule of V st the carrier of W1 = the carrier of W2 holds
W1 = W2
let V be RightMod of R; :: thesis: for W1, W2 being strict Submodule of V st the carrier of W1 = the carrier of W2 holds
W1 = W2
let W1, W2 be strict Submodule of V; :: thesis: ( the carrier of W1 = the carrier of W2 implies W1 = W2 )
assume the carrier of W1 = the carrier of W2 ; :: thesis: W1 = W2
then ( W1 is Submodule of W2 & W2 is Submodule of W1 ) by Th27;
hence W1 = W2 by Th25; :: thesis: verum