reserve a,b,c for set;

theorem Th3:
  for X being set st for a being set st a in X holds a is cardinal
  number holds union X is cardinal number
proof
  let X be set such that
A1: for a being set st a in X holds a is cardinal number;
  now
    let a;
    assume
A2: a in X;
    then a is cardinal number by A1;
    hence ex b being set st b in X & a c= b & b is cardinal set by A2;
  end;
  hence thesis by CARD_LAR:32;
end;
