reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem
  f is one-to-one implies for x,y holds [y,x] in f" iff [x,y] in f
proof
  assume
A1: f is one-to-one;
  let x,y;
  dom(f") = rng(f) by A1,FUNCT_1:33;
  then y in dom(f") & x = (f").y iff x in dom f & y = f.x by A1,FUNCT_1:32;
  hence thesis by FUNCT_1:1;
end;
