More correctly, to this end; or with a view to this.
We labor and strive (κοπιῶμεν καὶ ἀγωνιζόμεθα)
Both Pauline words. See on Col 1:29, where the two are found together as here. Also on κόπου labor, 1Th 1:3, and κοπιῶντας, and laboring 1Th 5:12. Comp. 1Ti 5:17, and 2Ti 2:6. Both words denote strenuous and painful effort. The καὶ; has an ascensive force: “we labor, yea struggle.”
We trust in (ἠλπίκαμεν ἐπὶ)
Better, have set our hope on. The verb with ἐπὶ in Pastorals, in Paul, Rom 15:12, a citation, and in 1Pe 1:13.