Metamath Proof Explorer


Definition df-p1

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

Ref Expression
Assertion df-p1
|- 1. = ( p e. _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 e. _V |-> ( ( lub ` p ) ` ( Base ` p ) ) )
10 0 9 wceq
 |-  1. = ( p e. _V |-> ( ( lub ` p ) ` ( Base ` p ) ) )