MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-p0 Structured version   Visualization version   GIF version

Definition df-p0 17238
Description: Define poset zero. (Contributed by NM, 12-Oct-2011.)
Assertion
Ref Expression
df-p0 0. = (𝑝 ∈ V ↦ ((glb‘𝑝)‘(Base‘𝑝)))

Detailed syntax breakdown of Definition df-p0
StepHypRef Expression
1 cp0 17236 . 2 class 0.
2 vp . . 3 setvar 𝑝
3 cvv 3338 . . 3 class V
42cv 1629 . . . . 5 class 𝑝
5 cbs 16057 . . . . 5 class Base
64, 5cfv 6047 . . . 4 class (Base‘𝑝)
7 cglb 17142 . . . . 5 class glb
84, 7cfv 6047 . . . 4 class (glb‘𝑝)
96, 8cfv 6047 . . 3 class ((glb‘𝑝)‘(Base‘𝑝))
102, 3, 9cmpt 4879 . 2 class (𝑝 ∈ V ↦ ((glb‘𝑝)‘(Base‘𝑝)))
111, 10wceq 1630 1 wff 0. = (𝑝 ∈ V ↦ ((glb‘𝑝)‘(Base‘𝑝)))
Colors of variables: wff setvar class
This definition is referenced by:  p0val  17240
  Copyright terms: Public domain W3C validator