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 Th9:
  (cod m <> {} or dom m = {}) & m`2 is Function of dom m,cod m
proof
  consider f, A,B such that
A1: m = [[A,B],f] and
A2: ( B = {} implies A = {})& f is Function of A,B by Th4;
  thus thesis by A1,A2;
end;
