reserve A,B,C,D,E for non empty set,
  a for Element of A,
  b for Element of B,
  c for Element of C,
  d for Element of D,
  X,Y,Z,S for set,x,y,z,s,t for object;

theorem Th2:
  for f1,f2 being Function of [:A,B,C:],D st for a,b,c holds f1.[a,
  b,c] = f2.[a,b,c] holds f1 = f2
proof
  let f1,f2 be Function of [:A,B,C:],D;
  assume for a,b,c holds f1.[a,b,c] = f2.[a,b,c];
  then for x,y,z st x in A & y in B & z in C holds f1.[x,y,z] = f2.[x,y,z];
  hence thesis by Th1;
end;
