reserve V for non empty set,
  A,B,A9,B9 for Element of V;
reserve f,f9 for Element of Funcs(V);
reserve m,m1,m2,m3,m9 for Element of Maps V;

theorem Th20:
  m in Maps(A,B) implies m`2 in Funcs(A,B)
proof
  assume
A1: m in Maps(A,B);
  then
A2: m = [[A,B],m`2] by Th16;
  then
A3: m`2 is Function of A,B by A1,Lm4;
  B = {} implies A = {} by A1,A2,Lm4;
  hence thesis by A3,FUNCT_2:8;
end;
