reserve X,Y,Z,X1,X2,Y1,Y2 for set, x,y,z,t,x1,x2 for object,
  f,g,h,f1,f2,g1,g2 for Function;

theorem Th49:
  X c= Y implies Funcs(Z,X) c= Funcs(Z,Y)
proof
  assume
A1: X c= Y;
  let x be object;
  assume x in Funcs(Z,X);
  then consider f such that
A2: x = f & dom f = Z and
A3: rng f c= X by FUNCT_2:def 2;
  rng f c= Y by A1,A3;
  hence thesis by A2,FUNCT_2:def 2;
end;
