1 Thessalonians 5:9-11
For God has not destined us for wrath, but for obtaining salvation through our Lord Jesus Christ, 10 who died for us, that whether we are awake or asleep, we may live together with Him. 11 Therefore encourage one another, and build up one another, just as you also are doing. NASB
In these verses we clearly see the rapture of the church, which is “salvation through our Lord Jesus Christ.”
In verses 1 through 5 of 1 Thessalonians 5, Paul talks about the “day of the Lord,” which is the day of wrath just after the tribulation (or I think it could mean the entire second half of the tribulation, which is called the great tribulation). And he assured the Thessalonians that because they were not of the darkness (not unbelievers), the day of the Lord would not overtake them (they would not have to experience it).
Now as to the times and the epochs, brethren, you have no need of anything to be written to you. 2 For you yourselves know full well that the day of the Lord will come just like a thief in the night. 3 While they are saying, “Peace and safety!” then destruction will come upon them suddenly like birth pangs upon a woman with child; and they shall not escape. 4 But you, brethren, are not in darkness, that the day should overtake you like a thief; 5 for you are all sons of light and sons of day. We are not of night nor of darkness ( 1 Thess. 5:1-5; NASB; bold for emphasis).
Then Paul gives them these instructions in verses 6 through 8 regarding how they should live, since they were believers.
So then let us not sleep as others do, but let us be alert and sober. 7 For those who sleep do their sleeping at night, and those who get drunk get drunk at night. 8 But since we are of the day, let us be sober, having put on the breastplate of faith and love, and as a helmet, the hope of salvation (1 Thess. 5:6-8; NASB).
They were to be alert and sober (self-controlled). And they were to put on the breastplate of faith and love and the helmet of salvation. In other word, they were to trust in His promises, love God, and be assured of their salvation.
Then Paul, in verses 9 and 10, continues to speak of the hope of our salvation in terms of the rapture. Hence, His return for us in the rapture is when our salvation is completed. And I say that he is speaking in terms of the rapture, because of his language used in verse 10—“that whether we are awake or asleep, we may live together with Him.” This language is the same as in 1Thessalonians 4:16-17, where he said, “The dead in Christ shall rise first. Then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air, and thus we shall always be with the Lord.” It is the same thought.
Also, we can see that verse 11 is very similar to 1 Thessalonians 4:18. Thus, in 1 Thessalonians 4:18, just as Paul tells them to comfort one another with these words—words of the rapture, in 1 Thessalonians 5:11, he similarly tells them to encourage (or comfort) one another. The thought is the same. And so we can conclude from all this that verses 9 and 10 are speaking of the rapture.