I feel sure that as recorded in John 8, when Jesus said several times in different ways "I am" He is alluding to the authority He came with to speak to Israel being like that of Moses, except in this case God did not just send Him but was in Him. And as Jesus sends any of us, or simply as we experientially know Him, in turn He is in us. And as we know Jesus experientially, so by proxy we are knowing God because He know God fully. So when Jesus says 'I am' it is because He is full of the experiential knowledge of God, of who God is.
