let V be Z_Module; :: thesis: for W1, W2 being Submodule of V holds W1 /\ W2 is Submodule of W1
let W1, W2 be Submodule of V; :: thesis: W1 /\ W2 is Submodule of W1
the carrier of (W1 /\ W2) c= the carrier of W1 by Lm8;
hence W1 /\ W2 is Submodule of W1 by Th43; :: thesis: verum