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Definition df-plt 17563
 Description: Define less-than ordering for posets and related structures. Unlike df-base 16484 and df-ple 16580, 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 17546 . 2 class lt
2 vp . . 3 setvar 𝑝
3 cvv 3444 . . 3 class V
42cv 1537 . . . . 5 class 𝑝
5 cple 16567 . . . . 5 class le
64, 5cfv 6328 . . . 4 class (le‘𝑝)
7 cid 5427 . . . 4 class I
86, 7cdif 3881 . . 3 class ((le‘𝑝) ∖ I )
92, 3, 8cmpt 5113 . 2 class (𝑝 ∈ V ↦ ((le‘𝑝) ∖ I ))
101, 9wceq 1538 1 wff lt = (𝑝 ∈ V ↦ ((le‘𝑝) ∖ I ))
 Colors of variables: wff setvar class This definition is referenced by:  pltfval  17564
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