reserve x,y for object,X,Y,A,B,C,M for set;
reserve P,Q,R,R1,R2 for Relation;

theorem Th21:
  for A,B being set, R being Subset of [:A,B:] holds
    .:R is Function of bool A, bool rng R
proof
  let A,B be set, R be Subset of [:A,B:];
A1: dom .:R = bool A by Def1;
  rng.:R c= bool rng R by Th20;
  hence thesis by A1,FUNCT_2:def 1,RELSET_1:4;
end;
