theorem Th3:
  {A,B} on P iff A on P & B on P
proof
  thus {A,B} on P implies A on P & B on P
  proof
A1: A in {A,B} & B in {A,B} by TARSKI:def 2;
    assume {A,B} on P;
    hence thesis by A1;
  end;
  assume
A2: A on P & B on P;
  let C be POINT of S;
  assume C in {A,B};
  hence thesis by A2,TARSKI:def 2;
end;
