reserve x,y,z,w for ExtReal,
  r for Real;
reserve f,g for ExtReal;

theorem Th23:
  (x = +infty iff -x = -infty) & (x = -infty iff -x = +infty)
proof
  -x = +infty implies x = -infty
  proof
    assume -x = +infty;
    then --x = -infty by Def3;
    hence thesis;
  end;
  hence thesis by Th5;
end;
