let V be ComplexLinearSpace; :: thesis: for W being Subspace of V
for x being set st x in W holds
x in V
let W be Subspace of V; :: thesis: for x being set st x in W holds
x in V
let x be set ; :: thesis: ( x in W implies x in V )
assume x in W ; :: thesis: x in V
then A1: x in the carrier of W by STRUCT_0:def 5;
the carrier of W c= the carrier of V by Def8;
hence x in V by A1, STRUCT_0:def 5; :: thesis: verum