reserve m for Cardinal,
  A,B,C for Ordinal,
  x,y,z,X,Y,Z,W for set,
  f for Function;
reserve f,g for Function,
  L for Sequence,
  F for Cardinal-Function;
reserve U1,U2,U for Universe;

theorem Th59:
  X in U implies bool X in U & union X in U & meet X in U
proof
  assume
A1: X in U;
  hence bool X in U by CLASSES1:def 2;
  U = Rank On U by Th50;
  hence
A2: union X in U by A1,CLASSES1:35;
  meet X c= union X by SETFAM_1:2;
  hence thesis by A2,CLASSES1:def 1;
end;
