Faith VS Existence of God!!!

I just worked out this counter-argument to the existance of God this morning, and I wanted to sound it out with some people:

Proof by Contradiction:
(1 Given) Assume God exists.
(2 Doctrine) If God exists, then the existence of God is accepted by faith alone.
(3 Re-written) If God exists, then the existence of God cannot be proven.
(4 Logical Equivalent) If the existence of God can be proven, then God cannot exist.
(5 Re-written) If God exists, then God cannot exist.
(6 Contradiction) We have reached a contradiction, our assumption was false.

The one problem I can see with this is that it takes the doctrine of faith as a given. It seems to me either faith must be incorrect doctrine, or God must not exist. Does anyone see a flaw in my argument?