The atheist asserts that God does not exist. When he makes this statement he is making a truth claim. But in order for truth to exist, God must exist. If God does not exist there is no such thing as truth. Therefore when the atheist says God does not exist, he actually proves the existence of God.
God is the truth, he is the ultimate authority. If God did not exist there would be no basis for the categories of truth or falsehood. When an atheist makes a truth claim he is not living consistently within his own belief system.
A consistent atheist would actually have no basis for anything. He would be left with absurdity and nonsense. Without God there would be no ultimate meaning or purpose for anything. The only consistent response for an atheist to anything that happened would be, so what?
The atheist cannot live consistently within his own worldview. He must borrow from the Christian worldview in order to live his life. Atheists must assume the existence of God in order to deny the existence of God. So atheism actually proves the existence of God. An atheist cannot escape the fact that he is made in the image of God and must live in God's world.