Charlie is planning to invite four friends to a small dinner party. Unfortunately, her friends don't all get along with one another, and she doesn't expect them all to come. She knows that...

1.) Brad or Cate, and perhaps even both of them, will come

2.) If Brad comes then Andrew won't come

3.) If Dennis doesn't come then Cate won't come either

4.) If Dennis does come, then Andrew will come too

Charlie reasons that the following conclusion follows logically from premises (1)-(4)

5.) Either Andrew, Cate, and Dennis all come to her dinner party and Brad does not, or else Brad is the ONLY one who comes

How does (5) follow logically from (1)-(4)?