RE: FOR I KNOW THAT THIS SHALL TURN TO MY SALVATION THROUGH YOU PRAYER, AND THE SUPPLY OF THE SPIRIT OF JESUS CHRIST.
You have to see the entire passage in context to understand it:
(Philippians 1:15-27 NIV) It is true that some preach Christ out of envy and rivalry, but others out of goodwill. {16} The latter do so in love, knowing that I am put here for the defense of the gospel. {17} The former preach Christ out of selfish ambition, not sincerely, supposing that they can stir up trouble for me while I am in chains. {18} But what does it matter? The important thing is that in every way, whether from false motives or true, Christ is preached. And because of this I rejoice. Yes, and I will continue to rejoice, {19} for I know that through your prayers and the help given by the Spirit of Jesus Christ, what has happened to me will turn out for my deliverance. {20} I eagerly expect and hope that I will in no way be ashamed, but will have sufficient courage so that now as always Christ will be exalted in my body, whether by life or by death. {21} For to me, to live is Christ and to die is gain. {22} If I am to go on living in the body, this will mean fruitful labor for me. Yet what shall I choose? I do not know! {23} I am torn between the two: I desire to depart and be with Christ, which is better by far; {24} but it is more necessary for you that I remain in the body. {25} Convinced of this, I know that I will remain, and I will continue with all of you for your progress and joy in the faith, {26} so that through my being with you again your joy in Christ Jesus will overflow on account of me. {27} Whatever happens, conduct yourselves in a manner worthy of the gospel of Christ. Then, whether I come and see you or only hear about you in my absence, I will know that you stand firm in one spirit, contending as one man for the faith of the gospel