Using an exclamation mark like that is a pretty rare thing to do. You wouldn’t for example see this if one used the axiom of replacement. The only other axiom that would be in a comparable position is foundation but foundation almost never comes up in conventional mathematics.
Of course it’s worth noting that axiom of replacement doesn’t come up much either, though obviously the case there isn’t quite as extreme as with foundation.
Of course it’s worth noting that axiom of replacement doesn’t come up much either, though obviously the case there isn’t quite as extreme as with foundation.