Description: Define poset unit. (Contributed by NM, 22-Oct-2011)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-p1 | |- 1. = ( p e. _V |-> ( ( lub ` p ) ` ( Base ` p ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cp1 | |- 1. |
|
| 1 | vp | |- p |
|
| 2 | cvv | |- _V |
|
| 3 | club | |- lub |
|
| 4 | 1 | cv | |- p |
| 5 | 4 3 | cfv | |- ( lub ` p ) |
| 6 | cbs | |- Base |
|
| 7 | 4 6 | cfv | |- ( Base ` p ) |
| 8 | 7 5 | cfv | |- ( ( lub ` p ) ` ( Base ` p ) ) |
| 9 | 1 2 8 | cmpt | |- ( p e. _V |-> ( ( lub ` p ) ` ( Base ` p ) ) ) |
| 10 | 0 9 | wceq | |- 1. = ( p e. _V |-> ( ( lub ` p ) ` ( Base ` p ) ) ) |