let K be Ring; :: thesis: for V being LeftMod of K
for W1, W2, W3 being Subspace of V st W1 c= W2 holds
W1 /\ W3 c= W2 /\ W3
let V be LeftMod of K; :: thesis: for W1, W2, W3 being Subspace of V st W1 c= W2 holds
W1 /\ W3 c= W2 /\ W3
let W1, W2, W3 be Subspace of V; :: thesis: ( W1 c= W2 implies W1 /\ W3 c= W2 /\ W3 )
( W1 is Subspace of W2 implies W1 /\ W3 is Subspace of W2 /\ W3 ) by VECTSP_5:17;
hence ( W1 c= W2 implies W1 /\ W3 c= W2 /\ W3 ) by Def7; :: thesis: verum