reserve x for set;

theorem Th2:
  2\1={1}
proof
  thus 2\1 c= {1}
  proof
    let x be object;
    assume
A1: x in 2\1;
    then
A2: x=0 or x=1 by CARD_1:50,TARSKI:def 2;
    not x in {0} by A1,CARD_1:49,XBOOLE_0:def 5;
    hence thesis by A2,TARSKI:def 1;
  end;
  let x be object;
  assume x in {1};
  then
A3: x = 1 by TARSKI:def 1;
  then
A4: not x in {0} by TARSKI:def 1;
  x in {0,1} by A3,TARSKI:def 2;
  hence thesis by A4,CARD_1:49,50,XBOOLE_0:def 5;
end;
