let V be ComplexLinearSpace; :: thesis: for W1, W2 being strict Subspace of V st the carrier of W1 = the carrier of W2 holds
W1 = W2
let W1, W2 be strict Subspace of V; :: thesis: ( the carrier of W1 = the carrier of W2 implies W1 = W2 )
assume the carrier of W1 = the carrier of W2 ; :: thesis: W1 = W2
then ( W1 is Subspace of W2 & W2 is Subspace of W1 ) by Th47;
hence W1 = W2 by Th45; :: thesis: verum