 By hypothesis, I am justified in believing (C\(_1)\). Premise (C\(_2)\) is a certainty because it is analytically true. The argument from (C\(_1)\) and (C\(_2)\) to (C\(_3)\) is valid. Therefore, my degree of confidence in (C\(_3)\) must equal my degree of confidence in (C\(_1)\). Since we are also assuming that I gain sufficient justification for (C\(_4)\), it seems to follow that I am justified in believing (C\(_5)\) by modus ponens. Similar arguments will lead me to dismiss further evidence such as a phone call from the towing service and my failure to see my car when I confidently stride over to the parking lot.