let V be Z_Module; :: thesis: for W1, W2 being Submodule of V holds 0. W1 = 0. W2
let W1, W2 be Submodule of V; :: thesis: 0. W1 = 0. W2
thus 0. W1 = 0. V by Def9
.= 0. W2 by Def9 ; :: thesis: verum