reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem Th15:
  PFuncs(V,C) c= bool [:V,C:]
proof
  let x be object;
  assume x in PFuncs(V,C);
  then consider f being Function such that
A1: x = f and
A2: dom f c= V and
A3: rng f c= C by PARTFUN1:def 3;
A4: f c= [: dom f, rng f:] by RELAT_1:7;
  [:dom f, rng f:] c= [:V,C:] by A2,A3,ZFMISC_1:96;
  then f c= [:V,C:] by A4;
  hence thesis by A1;
end;
