reserve x for object;
reserve n for Nat;
reserve D for non empty set;
reserve p,q for PartialPredicate of D;
reserve D for set;

theorem
  for D being non empty set, f being BinominativeFunction of D holds
  id field f is BinominativeFunction of D
  proof
    let D be non empty set, f be BinominativeFunction of D;
    dom f c= D & rng f c= D by RELAT_1:def 19;
    then reconsider X = field f as Subset of D by XBOOLE_1:8;
    id X is BinominativeFunction of D;
    hence thesis;
  end;
