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Definition df-odu 16952
 Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 16956, oduleval 16954, and oduleg 16955 for its principal properties. EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 17011. (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 16951 . 2 class ODual
2 vw . . 3 setvar 𝑤
3 cvv 3173 . . 3 class V
42cv 1474 . . . 4 class 𝑤
5 cnx 15692 . . . . . 6 class ndx
6 cple 15775 . . . . . 6 class le
75, 6cfv 5804 . . . . 5 class (le‘ndx)
84, 6cfv 5804 . . . . . 6 class (le‘𝑤)
98ccnv 5037 . . . . 5 class (le‘𝑤)
107, 9cop 4131 . . . 4 class ⟨(le‘ndx), (le‘𝑤)⟩
11 csts 15693 . . . 4 class sSet
124, 10, 11co 6549 . . 3 class (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩)
132, 3, 12cmpt 4643 . 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
141, 13wceq 1475 1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
 Colors of variables: wff setvar class This definition is referenced by:  oduval  16953
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