V. 4 This verse stresses the importance of prayer in Paul’s ministry. Paul says the same thing in Eph. 1:15ff and Phil. 1: 3ff and in Col. 1:3ff.
v. 5 “hearing of your love and faith toward the Lord Jesus and toward all the saints.”
Philemon’s genuine love and faith in and towards the Lord Jesus resulted in his love for others. (Rom. 5:5; Gal. 5:6; 1 John 3:14)
Other instances of hearing about the love and service of believers in the NT –2nd John 4; 3rd John 3-4
v 6 – As a result of Philemon’s love and faith in and towards Jesus, he shares that faith. He becomes a doer as well as a hearer of God’s Word. (James 1:22) He puts his Christianity into practice.
Because he is “in Christ,” his faith has become effective, thus seeking to obey the admonition of Jesus, “If you love Me, you will (keep on keeping) My commandments.” (John 14:15)
This results in a life where one’s faith rubs off on those around him. Folks see you serving God and knowing that it is real for you can motivate others to seek to serve Jesus more and more.
It can result in striving to reach the lost and strengthen the saved. It will motivate us to help the lost out of the “kingdom of darkness and be conveyed to the kingdom of the Son of His love.” (Col. 1:12ff)
V. 7 – Can a Christian have joy in their lives because of the love another Christian shows in their live towards you?
He refreshed people (Phile. 7). “Refreshed” is a military term that speaks of an army resting from a march.