There are two arguments for Christianity that can properly be considered "proofs":
In regard to the first point - the entire corpus of a religious tradition being fulfilled in the way that Christ fulfilled the Old Testament is unlike any other religion in the world. That will be the focus of this section.
For a brief discussion of the second point, see Appendix I.
When you analyze other religions, and other religious scriptures, you will note that suspiciously absent is any type of future prophecy.
This is because the modus operandi of all of history's false prophets was to show up unannounced and unheralded, tell everyone that they now, at long last, have the truth from God, publish their formula to work your way to their concept of Heaven, and then die without rising from the dead.
Jesus is the only one to ever show up and say:
Matthew 5:17
17 Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil.
He is the only one to ever say something like this, actually do so, and then leave the Old Testament intact, in writing, so that anyone could read and verify what He said was true. He never had to claim "Everyone before me was wrong, but now I've got the truth!", which is what every false prophet in history has had to do, because they had no history, and nothing tying them back to the very beginning of the creation.
This is true of Muhammad, Buddha, the writers of the Vedas, and every religious charlatan to ever come before or after them. None of them have anything remotely like unto the Old Testament foretelling of their arrival, or giving details of their lives thousands of years before they show up, or even having a forerunner like John the Baptist announcing their arrivals.
Without exception, none of history's false prophets could foretell what would happen after they were going to die, and none of them could point back to dozens of men prophesying of their arrivals. They just showed up, spouted off, and died, without demonstrating any type of verifiable supernatural phenomena.
Some, like Muhammad, claimed that they had forerunners and prophets foretelling them, but as is covered in the final section of Why I'm Not a Muslim, the Bible that Muhammad said he affirmed, and testified of himself, has been "conveniently" totally corrupted and lost, so no one can verify his claims. This is the bait-and-switch that these false prophets have to perform, as none of them have the genuine testimony of history by a God who is outside of time.
The Bible is filled with prophecy. The prophecies of Christ in the Old Testament are nothing like a coin flip. Often, a single location is given, an explicit detail is provided, or even a year is given, each of which had thousands of potential outcomes. There are many entire themes which find their culmination and fulfillment in only Jesus Christ, and likewise, there are symbols embedded into every facet of the practices that God told the Jews to perform, which testify of Jesus Christ.
The purpose of this section will be to highlight these, to demonstrate that they are not vague, and not sparse. They blanket the entire Old Testament.
Many, including myself, when they first hear about a "historical case for the resurrection", are extremely skeptical that such a thing could ever be compelling. However, the approach is simply taking uncontroversial facts that we know from Scripture, and the first century, and drawing some rather simple conclusions.
Some of these "minimal facts" used to support the resurrection historically are:
Cumulatively, these facts can be used to support a very compelling case for the resurrection.
The above approach comes from who is indisputably the foremost Christian scholar on the resurrection, Gary Habermas, and the points are covered and developed in more detail in his book The Case for the Resurrection, and in much more detail in his magnum opus, On the Resurrection - Volume 1, Evidences. I recommend the The Case for the Resurrection especially as a "basic" book for any Christian's library.