
theorem 
for F being Field,
    E being FieldExtension of F holds E,E are_isomorphic_over F
proof
let F be Field, E be FieldExtension of F;
now let a be Element of F;
  F is Subring of E by FIELD_4:def 1;
  then the carrier of F c= the carrier of E by C0SP1:def 3;
  hence (id E).a = a by FUNCT_1:18;
  end;
then id E is F-fixing;
then id E is F-isomorphism;
hence thesis;
end;
