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Definition df-odu 18333
Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 18337, oduleval 18335, and oduleg 18336 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 18541. (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 18332 . 2 class ODual
2 vw . . 3 setvar 𝑤
3 cvv 3479 . . 3 class V
42cv 1538 . . . 4 class 𝑤
5 cnx 17231 . . . . . 6 class ndx
6 cple 17305 . . . . . 6 class le
75, 6cfv 6560 . . . . 5 class (le‘ndx)
84, 6cfv 6560 . . . . . 6 class (le‘𝑤)
98ccnv 5683 . . . . 5 class (le‘𝑤)
107, 9cop 4631 . . . 4 class ⟨(le‘ndx), (le‘𝑤)⟩
11 csts 17201 . . . 4 class sSet
124, 10, 11co 7432 . . 3 class (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩)
132, 3, 12cmpt 5224 . 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
141, 13wceq 1539 1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
Colors of variables: wff setvar class
This definition is referenced by:  oduval  18334
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