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Definition df-odu 18287
Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 18291, oduleval 18289, and oduleg 18290 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 18495. (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
StepHypRef Expression
1 codu 18286 . 2 class ODual
2 vw . . 3 setvar 𝑤
3 cvv 3461 . . 3 class V
42cv 1532 . . . 4 class 𝑤
5 cnx 17170 . . . . . 6 class ndx
6 cple 17248 . . . . . 6 class le
75, 6cfv 6549 . . . . 5 class (le‘ndx)
84, 6cfv 6549 . . . . . 6 class (le‘𝑤)
98ccnv 5677 . . . . 5 class (le‘𝑤)
107, 9cop 4636 . . . 4 class ⟨(le‘ndx), (le‘𝑤)⟩
11 csts 17140 . . . 4 class sSet
124, 10, 11co 7419 . . 3 class (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩)
132, 3, 12cmpt 5232 . 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
141, 13wceq 1533 1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
Colors of variables: wff setvar class
This definition is referenced by:  oduval  18288
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