let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF
for W1, W2 being Subspace of V holds (0). W1 = (0). W2
let V be non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for W1, W2 being Subspace of V holds (0). W1 = (0). W2
let W1, W2 be Subspace of V; :: thesis: (0). W1 = (0). W2
( (0). W1 = (0). V & (0). W2 = (0). V ) by Th47;
hence (0). W1 = (0). W2 ; :: thesis: verum