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Definition df-oppg 17977
Description: Define an opposite group, which is the same as the original group but with addition written the other way around. df-oppr 18825 does the same thing for multiplication. (Contributed by Stefan O'Rear, 25-Aug-2015.)
Assertion
Ref Expression
df-oppg oppg = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(+g‘ndx), tpos (+g𝑤)⟩))

Detailed syntax breakdown of Definition df-oppg
StepHypRef Expression
1 coppg 17976 . 2 class oppg
2 vw . . 3 setvar 𝑤
3 cvv 3391 . . 3 class V
42cv 1636 . . . 4 class 𝑤
5 cnx 16065 . . . . . 6 class ndx
6 cplusg 16153 . . . . . 6 class +g
75, 6cfv 6101 . . . . 5 class (+g‘ndx)
84, 6cfv 6101 . . . . . 6 class (+g𝑤)
98ctpos 7586 . . . . 5 class tpos (+g𝑤)
107, 9cop 4376 . . . 4 class ⟨(+g‘ndx), tpos (+g𝑤)⟩
11 csts 16066 . . . 4 class sSet
124, 10, 11co 6874 . . 3 class (𝑤 sSet ⟨(+g‘ndx), tpos (+g𝑤)⟩)
132, 3, 12cmpt 4923 . 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(+g‘ndx), tpos (+g𝑤)⟩))
141, 13wceq 1637 1 wff oppg = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(+g‘ndx), tpos (+g𝑤)⟩))
Colors of variables: wff setvar class
This definition is referenced by:  oppgval  17978
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