ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-oppr GIF version

Definition df-oppr 13193
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 13192 . 2 class oppr
2 vf . . 3 setvar 𝑓
3 cvv 2737 . . 3 class V
42cv 1352 . . . 4 class 𝑓
5 cnx 12453 . . . . . 6 class ndx
6 cmulr 12531 . . . . . 6 class .r
75, 6cfv 5216 . . . . 5 class (.r‘ndx)
84, 6cfv 5216 . . . . . 6 class (.r𝑓)
98ctpos 6244 . . . . 5 class tpos (.r𝑓)
107, 9cop 3595 . . . 4 class ⟨(.r‘ndx), tpos (.r𝑓)⟩
11 csts 12454 . . . 4 class sSet
124, 10, 11co 5874 . . 3 class (𝑓 sSet ⟨(.r‘ndx), tpos (.r𝑓)⟩)
132, 3, 12cmpt 4064 . 2 class (𝑓 ∈ V ↦ (𝑓 sSet ⟨(.r‘ndx), tpos (.r𝑓)⟩))
141, 13wceq 1353 1 wff oppr = (𝑓 ∈ V ↦ (𝑓 sSet ⟨(.r‘ndx), tpos (.r𝑓)⟩))
Colors of variables: wff set class
This definition is referenced by:  opprvalg  13194
  Copyright terms: Public domain W3C validator