A word appearing in the phrase inn đa v’im “(lit.) a mind (inn) there is in me = I have a good mind (to do so)” from Late Notes on Verb Structure (LVS) written in 1969 (PE22/165). This phrase was first written as inn no v’im with {no >>} đa (PE22/165 note #108). This alteration suggests that đa is a heavily eroded/mutated form of na- “to be”, perhaps particular to this idiomatic phrase. As a counter-argument, đa is being used here in an existential statement “there is = *exists”, and these same 1969 notes state that:

Stem of verb “exist” (have being in primary world of history) was √EŊE, distinct from √NA joining adjs./nouns/pronouns in statements (or wishes) asserting (or desiring) a thing to have a certain quality, or to be the same as another (PE22/147).

This means that (in Quenya at least) NA was not used for existential statements. This opens up the possibility that đa is a mutated form of *da- “exists” from an otherwise unattested root *√DA, the Sindarin equivalent of √EÑ. This is further supported by notes from 1969 stating that a verb is mutated if it is immediately following its subject, in this case inn (PE23/142). Compare also some difficult to read forms in Quenya prayers from the 1950s {dôd >> dád >> hae >>} no (VT44/22), which might be earlier instances of da-.

Neo-Sindarin: Of these possibilities, I currently favor the theory that da- is verb meaning “to exist”, unrelated to √NĀ.