Definition df-plt 18057

Description: Define less-than ordering for posets and related structures. Unlike df-base 16922 and df-ple 16991, 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

Step	Hyp	Ref	Expression
1		cplt 18035	. 2 class lt
2		vp	. . 3 setvar 𝑝
3		cvv 3433	. . 3 class V
4	2	cv 1538	. . . . 5 class 𝑝
5		cple 16978	. . . . 5 class le
6	4, 5	cfv 6437	. . . 4 class (le‘𝑝)
7		cid 5489	. . . 4 class I
8	6, 7	cdif 3885	. . 3 class ((le‘𝑝) ∖ I )
9	2, 3, 8	cmpt 5158	. 2 class (𝑝 ∈ V ↦ ((le‘𝑝) ∖ I ))
10	1, 9	wceq 1539	1 wff lt = (𝑝 ∈ V ↦ ((le‘𝑝) ∖ I ))

This definition is referenced by:  pltfval  18058