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 Th32:
  f is one-to-one implies rng f = dom(f") & dom f = rng(f")
proof
  assume f is one-to-one;
  then f" = f~ by Def5;
  hence thesis by RELAT_1:20;
end;
