theorem
  Lin(A) = V implies ex I st I c= A
proof
  assume Lin(A) = V;
  then consider B such that
A1: B c= A and
A2: B is linearly-independent & Lin(B) = V by Th25;
  reconsider B as Basis of V by A2,Def3;
  take B;
  thus thesis by A1;
end;
