let V be strict ComplexLinearSpace; :: thesis: for W being strict Subspace of V st the carrier of W = the carrier of V holds
W = V
let W be strict Subspace of V; :: thesis: ( the carrier of W = the carrier of V implies W = V )
assume A1: the carrier of W = the carrier of V ; :: thesis: W = V
V is Subspace of V by Th44;
hence W = V by A1, Th49; :: thesis: verum