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Mirrors > Home > MPE Home > Th. List > df-p1 | Structured version Visualization version GIF version |
Description: Define poset unit. (Contributed by NM, 22-Oct-2011.) |
Ref | Expression |
---|---|
df-p1 | ⊢ 1. = (𝑝 ∈ V ↦ ((lub‘𝑝)‘(Base‘𝑝))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cp1 17757 | . 2 class 1. | |
2 | vp | . . 3 setvar 𝑝 | |
3 | cvv 3397 | . . 3 class V | |
4 | 2 | cv 1541 | . . . . 5 class 𝑝 |
5 | cbs 16579 | . . . . 5 class Base | |
6 | 4, 5 | cfv 6333 | . . . 4 class (Base‘𝑝) |
7 | club 17661 | . . . . 5 class lub | |
8 | 4, 7 | cfv 6333 | . . . 4 class (lub‘𝑝) |
9 | 6, 8 | cfv 6333 | . . 3 class ((lub‘𝑝)‘(Base‘𝑝)) |
10 | 2, 3, 9 | cmpt 5107 | . 2 class (𝑝 ∈ V ↦ ((lub‘𝑝)‘(Base‘𝑝))) |
11 | 1, 10 | wceq 1542 | 1 wff 1. = (𝑝 ∈ V ↦ ((lub‘𝑝)‘(Base‘𝑝))) |
Colors of variables: wff setvar class |
This definition is referenced by: p1val 17761 |
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