Months ago, I lookt up John 15 in order to confirm a similarity to verses 4-5 in a hymn text I was translating (
"Du Lebensbrod, Herr Jesu" by Johann Rist). Specifically, I referenced the NKJV, in which verse 5 appears as:
"I am the vine, you are the branches. He who abides in Me, and I in him, bears much fruit; for without Me you can do nothing."
The italics indicate a word that's supplied in the NKJV translation that's not in the Greek:
ἐγώ εἰμι ἡ ἄμπελος, ὑμεῖς τὰ κλήματα. ὁ μένων ἐν ἐμοὶ κἀγὼ ἐν αὐτῷ, οὗτος φέρει καρπὸν πολύν· ὅτι χωρὶς ἐμοῦ οὐ δύνασθε ποιεῖν οὐδέν.
The verb is explicit in the first clause ("'I am the vine'"), but it's merely implied in the second ("'you [are] the branches'"). The same is true of the Latin Vulgate:
ego sum vitis vos palmites qui manet in me et ego in eo hic fert fructum multum quia sine me nihil potestis facere
By itself, "you the branches" is just a phrase. Semantically, it can't stand by itself (formally speaking, at least). The preceding "I am the vine" sets up an instance of ellipsis, indicating that the copulative verb is implied and that this is, in fact, a complete clause. Grammatically, then, the second clause has a sort of dependence on the first to make its meaning clear, and this matches the broader idea behind the metaphor here ("'without Me you can do nothing'").
According to my Greek textbook (
New Testament Greek for Laymen: An Introductory Grammar by Michael A. Merritt, which I got as a .pdf for free from
the Daily Dose of Greek website), "Greek differs from English in that the verb εἰμί (to be) may be omitted from a sentence if it is understood from the context" (p. 54), so I'm not sure how applicable my comments are to the Greek (or to the Latin, which I think is comparable in this regard).