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Definition df-oppr 13238
Description: Define an opposite ring, which is the same as the original ring but with multiplication written the other way around. (Contributed by Mario Carneiro, 1-Dec-2014.)
Assertion
Ref Expression
df-oppr oppr = (𝑓 ∈ V ↦ (𝑓 sSet ⟨(.rβ€˜ndx), tpos (.rβ€˜π‘“)⟩))

Detailed syntax breakdown of Definition df-oppr
StepHypRef Expression
1 coppr 13237 . 2 class oppr
2 vf . . 3 setvar 𝑓
3 cvv 2737 . . 3 class V
42cv 1352 . . . 4 class 𝑓
5 cnx 12458 . . . . . 6 class ndx
6 cmulr 12536 . . . . . 6 class .r
75, 6cfv 5216 . . . . 5 class (.rβ€˜ndx)
84, 6cfv 5216 . . . . . 6 class (.rβ€˜π‘“)
98ctpos 6244 . . . . 5 class tpos (.rβ€˜π‘“)
107, 9cop 3595 . . . 4 class ⟨(.rβ€˜ndx), tpos (.rβ€˜π‘“)⟩
11 csts 12459 . . . 4 class sSet
124, 10, 11co 5874 . . 3 class (𝑓 sSet ⟨(.rβ€˜ndx), tpos (.rβ€˜π‘“)⟩)
132, 3, 12cmpt 4064 . 2 class (𝑓 ∈ V ↦ (𝑓 sSet ⟨(.rβ€˜ndx), tpos (.rβ€˜π‘“)⟩))
141, 13wceq 1353 1 wff oppr = (𝑓 ∈ V ↦ (𝑓 sSet ⟨(.rβ€˜ndx), tpos (.rβ€˜π‘“)⟩))
Colors of variables: wff set class
This definition is referenced by:  opprvalg  13239
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