let V be ComplexLinearSpace; :: 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
thus 0. W1 = 0. V by Def8
.= 0. W2 by Def8 ; :: thesis: verum