Jesus said this:
I am the Vine, you are the branches. He who abides in Me, and I in Him, brings forth much fruit, for without Me, you can do nothing (No Thing...Not Even One Thing...).
Earlier, Jesus had said, "I am the true Vine, and my Father is the Vinedresser..."
Jesus' point is this: the branches of a vine have a "derived life," a life communicated by the vine. Cut them off from the vine, lay them aside, and they wither and die. So it is with us. Our life is not only from Him, as an independent thing, it is from Him, in that it streams continuously from Him.
He says, "The Son has life in Himself." What He means is that, like the vine, he is the continuous source of life and spiritual health. And just as fruit is the product of a healthy vine with healthy branches, so spiritual fruit is the product of our connection with Him. If we are taken from Him, we die. Which is why it is so wonderful that HE has said, "He who comes to Me, I will never cast out." Almost everyone who's reading this blog does so via an internet connection. The life we derive from Jesus Christ is very much like streaming video. If the connection is broken, the video stops, and we have no way of seeing it until the connection is re-established. However, the connection with Him is "always on," if we let it be so. We CAN cut it off, just as you can choose to stop watching YouTube and go on a walk, but with Him, there's no "broken connection" necessary. We are a "hotspot" that can always communicate with the Son and the Father--and that connection is what brings fruit--the fact that we are tied to Him, and "always on."
This is an amazing truth--for no man, angel, demon, or circumstance can break that connection. Romans 8 says that "no created thing" shall be able to separate us from the love of God in Christ Jesus, and it's completely true. Not one entity or thing in the universe can separate us from Him once we have established a connection with Him. Since He lives "by the power of an endless life (or "indestructible life")", we cannot lose our lives with and in Him by any means. He is never "off" (back to the internet metaphor), He is always "on," with never a power outage, a denial of service attack, or a breakdown in software or hardware. NOTHING can stop the power of His life in us, unless we reject it.