reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve K,K1,K2,K3 for Field;
reserve SK1,SK2 for Subfield of K;
reserve ek,ek1,ek2 for Element of K;

theorem Th3:
  K1 is Subfield of K2 implies for x st x in K1 holds x in K2
  proof
    assume K1 is Subfield of K2;
    then A1: the carrier of K1 c= the carrier of K2 by Def1;
    for x st x in K1 holds x in K2
    by A1;
    hence thesis;
  end;
