reserve B for non empty set,
  A,X,x for set;

theorem Th2:
  for A,B being set holds Funcs(A,B) c= bool [:A,B:]
proof
  let A,B be set, x be object;
  assume x in Funcs(A,B);
  then consider f being Function such that
A1: x = f and
A2: dom f = A and
A3: rng f c= B by FUNCT_2:def 2;
A4: f c= [: dom f, rng f:] by RELAT_1:7;
  [:dom f, rng f:] c= [:A,B:] by A2,A3,ZFMISC_1:95;
  then f c= [:A,B:] by A4;
  hence thesis by A1;
end;
