reserve x for set;

theorem Th3:
  3\1 = {1,2}
proof
  thus 3\1 c= {1,2}
  proof
    let x be object;
    assume
A1: x in 3\1;
    then
A2: x=0 or x=1 or x=2 by CARD_1:51,ENUMSET1:def 1;
    not x in {0} by A1,CARD_1:49,XBOOLE_0:def 5;
    hence thesis by A2,TARSKI:def 1,def 2;
  end;
  thus {1,2} c= 3\1
  proof
    let x be object;
    assume x in {1,2};
    then
A3: x=1 or x=2 by TARSKI:def 2;
    then
A4: not x in {0} by TARSKI:def 1;
    x in {0,1,2} by A3,ENUMSET1:def 1;
    hence thesis by A4,CARD_1:49,51,XBOOLE_0:def 5;
  end;
end;
