reserve C for CatStr;
reserve f,g for Morphism of C;
reserve C for non void non empty CatStr,
  f,g for Morphism of C,
  a,b,c,d for Object of C;
reserve o,m for set;

theorem
  for a,b,c,d being Object of 1Cat(o,m) for f being Morphism of a,b for
  g being Morphism of c,d holds f=g
proof
  let a,b,c,d be Object of 1Cat(o,m);
  let f be Morphism of a,b;
  let g be Morphism of c,d;
  f = m by TARSKI:def 1;
  hence thesis by TARSKI:def 1;
end;
