"Proceedeth from"

as it is used in this verse, means,

Came from a person or place; came from; came forth.

...But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me...
...when he, the
Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
John 15:26 and John 16:13