Council of Orange, Chapter 24: Canon 24

Concerning the branches of the vine. The branches on the vine do not give life to the vine, but receive life from it; thus the vine is related to its branches in such a way that it supplies them with what they need to live, and does not take this from them. Thus it is to the advantage of the disciples, not Christ, both to have Christ abiding in them and to abide in Christ. For if the vine is cut down another can shoot up from the live root; but one who is cut off from the vine cannot live without the root (John 15:5ff).