He that overcometh (ho nikōn). Recalls the promises at the close of each of the Seven Letters in chapters 2 and 3.
Shall inherit (klēronomēsei). Future active of klēronomeō, word with great history (Mar 10:17; 1Pe 1:4; Gal 4:7; Rom 8:17), here interpreted for the benefit of these who share in Christ’s victory.
I will be his God (Esomai autōi theos). Repeated Old Testament promise (first to Abraham, Gen 17:7.). Cf. Rev 21:3.
He shall be my son (autos estai moi huios). Made first of Solomon (2Sa 7:14) and applied to David later in Psa 89:26.