theorem Th63:
  for G being set, H being non empty set for h being Function of G,H holds
  for g1 being Function of H,G holds
  h is bijective & g1 = h" implies g1 is bijective
proof
  let G be set,H be non empty set;
  let h be Function of G,H, g1 be Function of H,G;
  assume
A1: h is bijective & g1 = h";
  then dom h = G & rng g1 = dom h by FUNCT_1:33,FUNCT_2:def 1;
  hence thesis by A1,FUNCT_2:def 3;
end;
