There's no proof that Islam is an "Abrahamic religion," aside from an assertion made by Muslims that has no basis in history or theology (of either of the 3 faiths.)
"Abrahamic religions" as used in contemporary literature, is an interfaith term meant to show historical commonality and imply future reconciliation. However, it does not follow from this that it ought to be employed as either a historical or a heuristic category. All of these so called theologies and religious entities have persecuted each other for two millenniums non-stop, thus none of this is such a big deal. Yet, you are using this to alienate Islam. Lets see.
You think Christianity and Judaism are in one bracket in order to have more legitimacy to claim this name? Mate, Christianity has a trinitarian concept, and Abraham too according to Christian theology has to have worshipped this triune God head, or a God who had a son which the Jews would consider Blasphemy. What is your belief? That Jesus was there since the beginning with God and all things were created through him? Yes? Is that how Abraham would have believed?
In that case, Christianity should be alienated more than Islam because it is completely at loggerheads with Judaism. Of course intents are out in the open when someone brings a completely irrelevant subject and harps on it in a thread about Islam, its Sunnah, and how it does not go with a historical claim.
So your concept is "My Abraham is better than yours"!!!
You claimed earlier that Islam being an Abrahamic religion is an Islamic claim. False. This coinage came up in the 20th century. Though people wrote about this in the 19th century, also earlier, they referred to the Jewish abrahamic covenant, not all so called religions, and it was used by Christian writers.
Islam claims many prophets who are common, not only Abraham. So does Christianity. In fact, if you read the Qur'an it says no messenger of God is inferior or superior to humans. No one is supposed to make distinction of one against another. Terms used for messengers are just terms, and does not mean anyone is distinct. Thus, it is wrong to note that Islam falsely claims it is an Abrahamic religion which I think you have made in the haste of following through with your intent thus not very informed.
But if you really wish to argue this argument of yours that your Abraham is better than mine, then one could argue based on theology, and your theology is at loggerheads with the Jewish theology. Like chalk and cheese. Thus, if you again wish to argue your argument, Islamic theology is more in line with the Jewish theology, thus making "my Abraham, better than yours". Thats just an argument posed to show how arguments could be made to alienate rather than discuss the topic at hand. And again, it was Islam that claimed it is an abrahamic religion like Judaism and Christianity. Your statement shows that you have no clue of the Islamic theology or the Quran. Also you fail to see that Christianity has completely denied Jewish claims to their theology, called their Holy books "the Old Testament", denied their pure monotheism and imposed a trinity upon their scripture, yet claiming falsely that "my Abraham is better than yours".
For arguments Sake. Cheers.