reserve T for TopSpace;

theorem Th15:
  for F being Subset-Family of T holds union(Cl F) c= Cl(union F)
proof
  let F be Subset-Family of T;
  for A being set st A in Cl F holds A c= Cl(union F)
  proof
    let A be set;
    assume
A1: A in Cl F;
    then reconsider A0 = A as Subset of T;
    ex B being Subset of T st A0 = Cl B & B in F by A1,PCOMPS_1:def 2;
    hence thesis by PRE_TOPC:19,ZFMISC_1:74;
  end;
  hence thesis by ZFMISC_1:76;
end;
