Definition df-oppg 17776

Description: Define an opposite group, which is the same as the original group but with addition written the other way around. df-oppr 18623 does the same thing for multiplication. (Contributed by Stefan O'Rear, 25-Aug-2015.)

Assertion

Ref	Expression
df-oppg	|- oppg = ( w e. _V |-> ( w sSet <. ( +g ` ndx ) , tpos ( +g ` w ) >. ) )

Detailed syntax breakdown of Definition df-oppg

Step	Hyp	Ref	Expression
1		coppg 17775	. 2 class oppg
2		vw	. . 3 setvar w
3		cvv 3200	. . 3 class _V
4	2	cv 1482	. . . 4 class w
5		cnx 15854	. . . . . 6 class ndx
6		cplusg 15941	. . . . . 6 class +g
7	5, 6	cfv 5888	. . . . 5 class ( +g ` ndx )
8	4, 6	cfv 5888	. . . . . 6 class ( +g ` w )
9	8	ctpos 7351	. . . . 5 class tpos ( +g ` w )
10	7, 9	cop 4183	. . . 4 class <. ( +g ` ndx ) , tpos ( +g ` w ) >.
11		csts 15855	. . . 4 class sSet
12	4, 10, 11	co 6650	. . 3 class ( w sSet <. ( +g ` ndx ) , tpos ( +g ` w ) >. )
13	2, 3, 12	cmpt 4729	. 2 class ( w e. _V |-> ( w sSet <. ( +g ` ndx ) , tpos ( +g ` w ) >. ) )
14	1, 13	wceq 1483	1 wff oppg = ( w e. _V |-> ( w sSet <. ( +g ` ndx ) , tpos ( +g ` w ) >. ) )

This definition is referenced by:  oppgval  17777