J. Richey on Rm 8.10

Romans 8:10 (YLT) "and if Christ is in you, the body, indeed, is dead because of sin, and the Spirit is life because of righteousness,"

James Richey on Rom 8.10:

The context seems to suggest that the "spirit" is the Holy Spirit. There is nothing that indicates a change of the meaning of Spirit (HS) that is used throughout.  Rom 8.2 Spirit is HS; Rom 8.4 Spirit seems to be HS; Rom 8.5 Spirit is HS; Rom 8.6 Spirit is probably HS; Rom 8.9 Spirit is HS; Rom 8.10 Spirit is HS; Rom 8.11 Spirit is HS.

So if in the second clause (the Spirit is life because of righteousness) the word "spirit" refers to the Holy Spirit then it is He who is doing the action in the second clause. The Spirit (gives, grants, infuses, animates, is the source, or creates) life because of righteousness.  (This seems fairly certain to me, HS activity with life is implied.)

The first clause (although the body is dead because of sin) becomes tricky - because it is not strictly parallel.  The body is (subject to die, in the process of dying, in the midst of death) dead because of sin.

The first clause is about the human body, the second clause about the Holy Spirit. The first clause is about physical death, the second clause about eternal life.  The Greek word here for life, zoe, is nearly always used of eternal life, or the life of God in the New Testament, but only the context can tell us what it means here.

As far as Greek grammar goes, it is a bit different than what we might think. New Testament writers are not writing according to the rules of Greek grammar that have been written down. Those rules were written down much later reflecting the way people wrote. Paul as well as Peter, will write clauses that appear to be parallel - but interpretatively cannot be so, and were never intended to be seen as such.