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 ) ) ) |