"Proves"? The phrase you are looking for is "I have inferred..." If we insist on calling our inferences "proof," we will never be able to read scripture objectively. Instead, we will always try to find a way to force the scriptures to say something we've already concluded. Firstly, if we simply believe what's written in the Bible, do we need to be able to rationally explain it? In other words: is it okay for us to simply believe what God tells us about Himself without our needing to completely understand God? Is it okay if comprehension of God is beyond our reach? The scriptures do say that Jesus submitted to the Father. They also state that Jesus is God manifest in flesh. Your brothers and sisters here simply are simply reading what's stated in scripture and believing it. Why shouldn't that be enough? Secondly, would you be willing to accept that the inference you've made here is based on certain premises, but that there may be additional premises stated in scripture that may challenge the conclusions you've arrived at? In other words, will you allow yourself to experience doubt in order to objectively hear scriptures that sufficiently answer your question, "If Christ is God then how can he be lower than himself but head of himself at the same time"? If so, then I have some passages I'd like to discuss with you.