Let me clarify a few points I made before.
First, by saying that other religions have borrowed from the Bible's inspired authority from God, I am including both the Old and the New Testaments (if I understood your assertion correctly). By Scriptures own storyline, the Old and New Testaments are explicitly connected via the many prophecies given that foretold of the One Messiah who would come to be the Suffering Servant, to die on behalf of sinners in order to reconcile them with God by faith in the work of Christ. This much is clear as one sees the storyline unfold from covenant to covenant and God's purposes coming to fulfillment through His Son Jesus Christ, the true Jew.
Second, it is not only for a religion to claim such authority from God, but to make good on such claims. I know this sentence will be challenged, but the Scriptures have continually be tried, tested, argued against, and debated continually by some of the most fierce intellectuals. Yet, the Christian worldview has answered the challenges and also has shown how it practically is found and seen in all of life and experience. For example, in relation to life and experience, since we have all sinned against God and sought his own ways, man has sought to satisfy his heart with other things as Satan too seeks to deceive and misled many away from the One true Triune God. So, man does create religions contrary to who God has revealed Himself to be, does worship his own wisdom and self, does seek after pleasing himself rather than turning to His Creator to find ultimate joy and everlasting satisfaction.
It is for these other religions who claim such authority to make good on their claims in relation to life and reality, experience, consistency within its claims, and reason. Although there are some mysteries in Christianity that may not be resolvable (not to be confused with contradictions), Christianity has continually made good on its claims.
