reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

theorem Th43:
  for x,y being object holds [y,x] in dom ~f implies (~f).(y,x) = f.(x,y)
proof let x,y be object;
  assume [y,x] in dom ~f;
  then [x,y] in dom f by Th42;
  hence thesis by Def2;
end;
