
theorem Th19:
  for X being set holds union Fin X = X
proof
  let X be set;
  union Fin X c= union bool X by FINSUB_1:13,ZFMISC_1:77;
  hence union Fin X c= X by ZFMISC_1:81;
  let x be object;
  assume x in X;
  then {x} c= X by ZFMISC_1:31;
  then
A1: {x} in Fin X by FINSUB_1:def 5;
  x in {x} by TARSKI:def 1;
  hence thesis by A1,TARSKI:def 4;
end;
