Description: Define poset unit. (Contributed by NM, 22-Oct-2011)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-p1 | ⊢ 1. = ( 𝑝 ∈ 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 ∈ V ↦ ( ( lub ‘ 𝑝 ) ‘ ( Base ‘ 𝑝 ) ) ) | 
| 10 | 0 9 | wceq | ⊢ 1. = ( 𝑝 ∈ V ↦ ( ( lub ‘ 𝑝 ) ‘ ( Base ‘ 𝑝 ) ) ) |