reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem
  for o,m being object for c being Object of 1Cat(o,m) holds c = o
  proof
    let o,m be object;
    let c be Object of 1Cat(o,m);
    set C = 1Cat(o,m);
    C = CatStr(# { o },{ m },  m :-> o , m :-> o,(m,m):->m #) by CAT_1:def 11;
    hence thesis by TARSKI:def 1;
  end;
