Description: Expansion of an ordered pair when the second member is a proper class. See also opprc . (Contributed by NM, 15-Nov-1994) (Revised by Mario Carneiro, 26-Apr-2015)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | opprc2 | |- ( -. B e. _V -> <. A , B >. = (/) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpr | |- ( ( A e. _V /\ B e. _V ) -> B e. _V ) |
|
| 2 | opprc | |- ( -. ( A e. _V /\ B e. _V ) -> <. A , B >. = (/) ) |
|
| 3 | 1 2 | nsyl5 | |- ( -. B e. _V -> <. A , B >. = (/) ) |