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Definition df-plt 16879
Description: Define less-than ordering for posets and related structures. Unlike df-base 15786 and df-ple 15882, 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 16862 . 2 class lt
2 vp . . 3 setvar 𝑝
3 cvv 3186 . . 3 class V
42cv 1479 . . . . 5 class 𝑝
5 cple 15869 . . . . 5 class le
64, 5cfv 5847 . . . 4 class (le‘𝑝)
7 cid 4984 . . . 4 class I
86, 7cdif 3552 . . 3 class ((le‘𝑝) ∖ I )
92, 3, 8cmpt 4673 . 2 class (𝑝 ∈ V ↦ ((le‘𝑝) ∖ I ))
101, 9wceq 1480 1 wff lt = (𝑝 ∈ V ↦ ((le‘𝑝) ∖ I ))
Colors of variables: wff setvar class
This definition is referenced by:  pltfval  16880
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