
theorem Th3:
  for x being object holds x is ExtNat iff x is Nat or x = +infty
proof
  let x be object;
  hereby
    assume x is ExtNat;
    then x in NAT or x = +infty by Def1, ZFMISC_1:136;
    hence x is Nat or x = +infty;
  end;
  assume x is Nat or x = +infty;
  then x in NAT or x in {+infty} by ORDINAL1:def 12, TARSKI:def 1;
  then x in ExtNAT by XBOOLE_0:def 3;
  hence thesis;
end;
