To this end (eis touto). The godliness (eusebeia) of 1Ti 4:8. See 2Co 6:10 as Paul’s own commentary.
We labour (kopiōmen, Col 1:29) and strive (kai agōnizometha, Col 1:29). Both Pauline words.
Because we have set our hope (hoti elpikamen). Perfect active indicative of elpizō (Rom 15:12).
Saviour of all men (sōtēr pantōn anthrōpōn). See note on 1Ti 1:1 for sōtēr applied to God as here. Not that all men “are saved” in the full sense, but God gives life (1Ti 6:13) to all (Act 17:28).
Specially of them that believe (malista pistōn). Making a distinction in the kinds of salvation meant. “While God is potentially Saviour of all, He is actually Saviour of the pistoi” (White). So Jesus is termed “Saviour of the World” (Joh 4:42). Cf. Gal 6:10.