theorem Th159:
  z <> x implies (All(z,G) = All(z,H)/(x,y) iff G = H/(x,y))
proof
  assume
A1: z <> x;
  thus All(z,G) = All(z,H)/(x,y) implies G = H/(x,y)
  proof
    assume All(z,G) = All(z,H)/(x,y);
    then All(z,G) = All(z,H/(x,y)) by A1,Lm2;
    hence thesis by ZF_LANG:3;
  end;
  thus thesis by A1,Lm2;
end;
