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Definition df-oppr 18388
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 ⟨(.r‘ndx), tpos (.r𝑓)⟩))

Detailed syntax breakdown of Definition df-oppr
StepHypRef Expression
1 coppr 18387 . 2 class oppr
2 vf . . 3 setvar 𝑓
3 cvv 3168 . . 3 class V
42cv 1473 . . . 4 class 𝑓
5 cnx 15634 . . . . . 6 class ndx
6 cmulr 15711 . . . . . 6 class .r
75, 6cfv 5786 . . . . 5 class (.r‘ndx)
84, 6cfv 5786 . . . . . 6 class (.r𝑓)
98ctpos 7211 . . . . 5 class tpos (.r𝑓)
107, 9cop 4126 . . . 4 class ⟨(.r‘ndx), tpos (.r𝑓)⟩
11 csts 15635 . . . 4 class sSet
124, 10, 11co 6523 . . 3 class (𝑓 sSet ⟨(.r‘ndx), tpos (.r𝑓)⟩)
132, 3, 12cmpt 4633 . 2 class (𝑓 ∈ V ↦ (𝑓 sSet ⟨(.r‘ndx), tpos (.r𝑓)⟩))
141, 13wceq 1474 1 wff oppr = (𝑓 ∈ V ↦ (𝑓 sSet ⟨(.r‘ndx), tpos (.r𝑓)⟩))
Colors of variables: wff setvar class
This definition is referenced by:  opprval  18389
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