Let stand for the undecidable sentence constructed above, and assume for purposes of obtaining a contradiction that the consistency of the system can be proved from within the system itself. This is equivalent to proving the statement "System is consistent". Now consider the statement , where = "If the system is consistent, then is not provable". The proof of sentence can be formalized within the system , and therefore the statement , " is not provable", (or identically, "not ") can be proved in the system .
Let stand for the undecidable sentence constructed above, and assume for purposes of obtaining a contradiction that the consistency of the system can be proved from within the system itself. This is equivalent to proving the statement "System is consistent" Now consider the statement , where = "If the system is consistent, then is not provable". The proof of sentence can be formalized within the system , and therefore the statement , " is n.ot provable", (or identically, "not ") can be proved in the system .