reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;

theorem
  f is one-to-one implies (f")" = f
proof
  assume
A1: f is one-to-one;
  then rng f = dom(f") by Th32;
  then
A2: f*f" = id dom(f") by A1,Th38;
  dom f = rng(f") by A1,Th32;
  hence thesis by A1,A2,Th40;
end;
