let R be Ring; :: thesis: for V being RightMod of R
for W1, W2, W3 being Submodule of V st W1 is Submodule of W2 holds
W1 is Submodule of W2 + W3
let V be RightMod of R; :: thesis: for W1, W2, W3 being Submodule of V st W1 is Submodule of W2 holds
W1 is Submodule of W2 + W3
let W1, W2, W3 be Submodule of V; :: thesis: ( W1 is Submodule of W2 implies W1 is Submodule of W2 + W3 )
assume A1: W1 is Submodule of W2 ; :: thesis: W1 is Submodule of W2 + W3
W2 is Submodule of W2 + W3 by Th7;
hence W1 is Submodule of W2 + W3 by A1, RMOD_2:26; :: thesis: verum