One powerful way the attitude statements can be used whenever you're trying something that causes you moderate anxiety that you are nervous/anxious about. To help answer your question, I'll give you an example of when the attitude statements helped me.
Around the time I first started doing the therapy, I was invited by some co-workers to go play football with them and their friends every Saturday. Having barely known my co-workers (and not knowing their friends at all), I was pretty damn anxious about it...but I wanted to get over social anxiety, and meet new people. So, I decided I was going to take them up on their invitation and join them.
That first Saturday joining them in the football game, while driving there I stated the attitude statements out loud to myself, such as "So what? I'm just playing football with these guys...who cares? It's not that big a deal". You can probably see there that I incorporated 3 attitude statements into that sentence. I did this not only the first Saturday I played football with them, but also the next few Saturdays as well, each time stating the attitude statements out loud to myself. Even back then, with all my anxiety, I noticed that these statements had a huge effect on me, and I was able to meet new people and have fun playing football with people who I probably never would have even talked to before because of my anxiety. The attitude statements were that powerful for me.
So enough about me, but that's just an example of one significant way they can be used. They're extremely helpful when you will soon be presented with a social situation that you know will cause you anxiety. But you do not need to replace these with your old ANTs stoppage statements; these are just additional statements that can be used when you are going to be facing an event or situation that will cause you anxiety. And it doesn't have to be only when meeting new people; for example, if making phone calls causes you a lot of anxiety, but you know that there's a phone call that you need to make, then these attitude statements can be very helpful with that. They kind of break the anxiety down a bit, and start to make you think that the social things that we're used to feeling anxious about are probably not that big of a deal when it all comes down to it.