1 Corinthians 7:17 gives the general rule of remaining in one's calling, directly underlies the specific advice about slavery here.

1 Corinthians 7:20 commands remaining in one's calling, setting up the very next verse where Paul applies that to slaves.

In 1 Corinthians 12:13, Paul says all are baptized into one body, whether slave or free — the spiritual unity that underlies the counsel not to worry about status.

Galatians 3:28 declares no slave or free in Christ — this is the theological basis for not being concerned about one's slave status.

Philippians 4:6 again: 'do not be anxious' — a strong parallel to Paul's 'do not be concerned' for slaves, reinforcing the same principle.

Colossians 3:11 similarly abolishes slave/free distinctions in Christ, reinforcing that a slave's status is not ultimate — so don't be anxious.

Hebrews 13:5 calls for contentment in all circumstances, echoing Paul's advice here for slaves not to let their status trouble them.