Definition df-oppg 19364

Description: Define an opposite group, which is the same as the original group but with addition written the other way around. df-oppr 20334 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 (+g‘𝑤)⟩))

Detailed syntax breakdown of Definition df-oppg

Step	Hyp	Ref	Expression
1		coppg 19363	. 2 class oppg
2		vw	. . 3 setvar 𝑤
3		cvv 3480	. . 3 class V
4	2	cv 1539	. . . 4 class 𝑤
5		cnx 17230	. . . . . 6 class ndx
6		cplusg 17297	. . . . . 6 class +g
7	5, 6	cfv 6561	. . . . 5 class (+g‘ndx)
8	4, 6	cfv 6561	. . . . . 6 class (+g‘𝑤)
9	8	ctpos 8250	. . . . 5 class tpos (+g‘𝑤)
10	7, 9	cop 4632	. . . 4 class ⟨(+g‘ndx), tpos (+g‘𝑤)⟩
11		csts 17200	. . . 4 class sSet
12	4, 10, 11	co 7431	. . 3 class (𝑤 sSet ⟨(+g‘ndx), tpos (+g‘𝑤)⟩)
13	2, 3, 12	cmpt 5225	. 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(+g‘ndx), tpos (+g‘𝑤)⟩))
14	1, 13	wceq 1540	1 wff oppg = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(+g‘ndx), tpos (+g‘𝑤)⟩))

This definition is referenced by:  oppgval  19365