Acts 15:10 describes the yoke of the law that the council's letter relieves — the joy in v31 comes from freedom from that burden.

Acts 16:5 shows the result of the letter's encouragement — churches strengthened and growing.

Acts 13:48 shows Gentiles rejoicing at the gospel — v31 similarly records rejoicing among Gentile believers from the letter's affirmation.

Galatians 2:4 refers to false brethren seeking to impose bondage — the letter's consolation in v31 affirms freedom from such.

Galatians 2:5 shows Paul's refusal to submit to bondage — the letter's consolation in v31 is the fruit of that stand.

Galatians 5:1 commands standing in liberty — the letter's message in v31 is the basis for that freedom.