
theorem Th3:
  for n being Nat, x,y being object st n = {x,y} & x <> y
    holds (x = 0 & y = 1) or (x = 1 & y = 0)
   proof
     let n be Nat, x,y be object;
     assume
A1:  n = {x,y} & x <> y; then
     card n = 2 by CARD_2:57; then
A2:   x in {0,1} & y in {0,1} by A1,CARD_1:50,TARSKI:def 2;
     per cases by A2,TARSKI:def 2;
       suppose x = 0;
         hence thesis by A1,A2,TARSKI:def 2;
       end;
       suppose x = 1;
         hence thesis by A1,A2,TARSKI:def 2;
       end;
    end;
