Metamath Proof Explorer


Definition df-p1

Description: Define poset unit. (Contributed by NM, 22-Oct-2011)

Ref Expression
Assertion df-p1 1. = ( 𝑝 ∈ V ↦ ( ( lub ‘ 𝑝 ) ‘ ( Base ‘ 𝑝 ) ) )

Detailed syntax breakdown

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 ) ) )