theorem Th10:
  (for n holds B.n = A) implies Union B = A
proof
  assume
A1: for n holds B.n = A;
  now
    let x be object;
    assume x in rng B;
    then ex n st x = B.n by Th4;
    hence x = A by A1;
  end;
  then rng B = {A} by ZFMISC_1:35;
  then union rng B = A by ZFMISC_1:25;
  hence thesis by CARD_3:def 4;
end;
