Definition df-odu 17741

Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 17745, oduleval 17743, and oduleg 17744 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 17800. (Contributed by Stefan O'Rear, 29-Jan-2015.)

Assertion

Ref	Expression
df-odu	⊢ ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩))

Detailed syntax breakdown of Definition df-odu

Step	Hyp	Ref	Expression
1		codu 17740	. 2 class ODual
2		vw	. . 3 setvar 𝑤
3		cvv 3496	. . 3 class V
4	2	cv 1536	. . . 4 class 𝑤
5		cnx 16482	. . . . . 6 class ndx
6		cple 16574	. . . . . 6 class le
7	5, 6	cfv 6357	. . . . 5 class (le‘ndx)
8	4, 6	cfv 6357	. . . . . 6 class (le‘𝑤)
9	8	ccnv 5556	. . . . 5 class ◡(le‘𝑤)
10	7, 9	cop 4575	. . . 4 class ⟨(le‘ndx), ◡(le‘𝑤)⟩
11		csts 16483	. . . 4 class sSet
12	4, 10, 11	co 7158	. . 3 class (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩)
13	2, 3, 12	cmpt 5148	. 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩))
14	1, 13	wceq 1537	1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩))

This definition is referenced by:  oduval  17742