reserve x,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,y for object, X,Z for set;

theorem Th2:
  { x1,x2,x3 } = { x1 } \/ { x2,x3 }
proof
  now
    let x be object;
    x in { x1,x2,x3 } iff x=x1 or x=x2 or x=x3 by Def1;
    then x in { x1,x2,x3 } iff x in { x1 } or x in { x2,x3 } by TARSKI:def 1
,def 2;
    hence x in { x1,x2,x3 } iff x in { x1 } \/ { x2,x3 } by XBOOLE_0:def 3;
  end;
  hence thesis by TARSKI:2;
end;
