How does the Bible prove other religions are false?
The Bible proves which religions are false by showing in detail what the true plan of God is. Whatever does not square up with truth is false. At the center of this plan is the ransom of Jesus, something all religions do not claim.
Please read 1 Corinthians chapter 15, in which the Apostle Paul brilliantly describes the whole plan: Christ died for our sins, was buried, rose on the third day, was seen by the Apostles (vs. 14 “…and if Christ is not risen, then is our preaching vain, and your faith is also vain.”). There would be false witnesses, the firstfruits (church class) would rise, then the resurrection of all man (vs. 22 “For as in Adam all die, even so in Christ shall all be made alive.”) and the last enemy to be destroyed is death (vs. 26) and all things are presented to Jehovah after the Little Season – the world finally at one with God – paradise restored. Vs. 28 has an interesting phrase – that God may be “all in all.” This literally means “everything to everyone.” He will be everything we need in all possible ways. How beautiful!