Quoted from Psalm 110:1.
“by the holy spirit.” David spoke as God directed him to via the gift of holy spirit that was upon David (see commentary on Matt. 22:43). Even though the Greek has both articles with holy spirit, tō pneuma tō hagion (τῷ πνεύματι τῷ ἁγίω), it seems to be more of a reference to the gift of holy spirit than it is to the Giver, God. There are many other times the gift of holy spirit has both articles (cp. Luke 3:22; John 14:26; Acts 2:33; 5:32; 10:44, 47; 11:15; 15:8; 19:6; Eph. 1:13; 1 Thess. 4:8). [For more information on the uses of “Holy Spirit”, see Appendix 6: “Usages of ‘Spirit.’” For more information on the Holy Spirit, see Appendix 11: “What is the Holy Spirit”].