Description: The class abstraction defined by a formula not containing the abstraction variable is either the empty set or the universal class. (Contributed by Mario Carneiro, 29-Aug-2013) (Revised by BJ, 22-Mar-2020)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ab0orv | |- ( { x | ph } = _V \/ { x | ph } = (/) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfv | |- F/ x ph |
|
| 2 | dfnf5 | |- ( F/ x ph <-> ( { x | ph } = _V \/ { x | ph } = (/) ) ) |
|
| 3 | 1 2 | mpbi | |- ( { x | ph } = _V \/ { x | ph } = (/) ) |