
theorem
  for X being set
  st (ex Y being Graph-membered set st Y in X)
  holds meet X is Graph-membered
proof
  let X be set;
  assume A1: ex Y being Graph-membered set st Y in X;
  let x be object;
  assume x in meet X;
  then A2: for Y being set holds Y in X implies x in Y by SETFAM_1:def 1;
  consider Y being Graph-membered set such that
    A3: Y in X by A1;
  thus thesis by A2, A3, Def1;
end;
