Is 1 Thessalonians 4 part of the mystery Paul revealed about the rapture?
Yes. Though the word 'mystery' is not used in 1 Thessalonians 4, the passage addresses the same truth revealed to Paul, the outcalling or rapture of the church. It parallels 1 Corinthians 15, including the promise that believers who have died will not be without hope.
Les teaches that although 1 Thessalonians 4 does not use the word 'mystery,' Paul is talking about the same thing, so it is part of the mystery—the secret revealed to the apostle Paul. That mystery is what Les calls the outcalling or rapture of the church. In 1 Thessalonians 4:13, Paul says he would not have believers ignorant concerning those who are asleep, so they need not sorrow as others who have no hope. Les calls this the qualifications for the rapture: believing that Jesus died and rose again.
But I would not have you to be ignorant, brethren, concerning them which are asleep, that ye sorrow not, even as others which have no hope.
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Is 1 Thessalonians 4 part of the rapture mystery even though it doesn't use the word mystery?
First Thessalonians 4 does not use the word 'mystery,' but it describes the same event, which is called the outcalling or the rapture of the church.