
theorem Th1:
  for X being set for A being Subset-Family of X holds A c= UniCl A
proof
  let X be set;
  let A be Subset-Family of X;
  let x be object;
  assume
A1: x in A;
  then reconsider x9=x as Subset of X;
  reconsider s = {x9} as Subset-Family of X by SUBSET_1:41;
A2: x = union s by ZFMISC_1:25;
  s c= A by A1,ZFMISC_1:31;
  hence thesis by A2,Def1;
end;
