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

Definition df-plt 17558
Description: Define less-than ordering for posets and related structures. Unlike df-base 16479 and df-ple 16575, this is a derived component extractor and not an extensible structure component extractor that defines the poset. (Contributed by NM, 12-Oct-2011.) (Revised by Mario Carneiro, 8-Feb-2015.)
Assertion
Ref Expression
df-plt lt = (𝑝 ∈ V ↦ ((le‘𝑝) ∖ I ))

Detailed syntax breakdown of Definition df-plt
StepHypRef Expression
1 cplt 17541 . 2 class lt
2 vp . . 3 setvar 𝑝
3 cvv 3495 . . 3 class V
42cv 1527 . . . . 5 class 𝑝
5 cple 16562 . . . . 5 class le
64, 5cfv 6349 . . . 4 class (le‘𝑝)
7 cid 5453 . . . 4 class I
86, 7cdif 3932 . . 3 class ((le‘𝑝) ∖ I )
92, 3, 8cmpt 5138 . 2 class (𝑝 ∈ V ↦ ((le‘𝑝) ∖ I ))
101, 9wceq 1528 1 wff lt = (𝑝 ∈ V ↦ ((le‘𝑝) ∖ I ))
Colors of variables: wff setvar class
This definition is referenced by:  pltfval  17559
  Copyright terms: Public domain W3C validator