Although I brought this up in the comments, I would like to refute a particular argument advanced by MethoDeist:
Your logical progression is correct but not on objective level because no religion can be proven as correct/incorrect. It is correct on a personal (subjective) level.
It is not necessary to prove that intellectual assertions are true or false in order to prove that they contradict each other.
1. Gavin Richardson has the UMC logo tattooed on his butt.
2. Gavin Richardson does not have the UMC logo tattooed on his butt.
I have not done any research on the subject. Nor do I plan to, or wish to hear from anyone who has. But I don't have to in order to prove that there are only two possibilities: 1 or 2.
If there is a third possibility, please inform me of it. If you cannot, then you must accept my argument as correct.
3. Religion A says that all religions except itself are false.
4. Religion B says that all religions except itself are false.
...then it is not necessary for me to prove the accuracy of the claims of either Religions A or B in order to prove that they contradict each other at an objective level.