let K be Ring; :: thesis: for V being LeftMod of K
for W1, W3, W2 being Subspace of V st W1 c= W3 holds
W1 /\ W2 c= W3
let V be LeftMod of K; :: thesis: for W1, W3, W2 being Subspace of V st W1 c= W3 holds
W1 /\ W2 c= W3
let W1, W3, W2 be Subspace of V; :: thesis: ( W1 c= W3 implies W1 /\ W2 c= W3 )
( W1 is Subspace of W3 implies W1 /\ W2 is Subspace of W3 ) by VECTSP_5:18;
hence ( W1 c= W3 implies W1 /\ W2 c= W3 ) by Def7; :: thesis: verum