Definition df-oppr 13624

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 e. _V |-> ( f sSet <. ( .r ` ndx ) , tpos ( .r ` f ) >. ) )

Detailed syntax breakdown of Definition df-oppr

Step	Hyp	Ref	Expression
1		coppr 13623	. 2 class oppr
2		vf	. . 3 setvar f
3		cvv 2763	. . 3 class _V
4	2	cv 1363	. . . 4 class f
5		cnx 12675	. . . . . 6 class ndx
6		cmulr 12756	. . . . . 6 class .r
7	5, 6	cfv 5258	. . . . 5 class ( .r ` ndx )
8	4, 6	cfv 5258	. . . . . 6 class ( .r ` f )
9	8	ctpos 6302	. . . . 5 class tpos ( .r ` f )
10	7, 9	cop 3625	. . . 4 class <. ( .r ` ndx ) , tpos ( .r ` f ) >.
11		csts 12676	. . . 4 class sSet
12	4, 10, 11	co 5922	. . 3 class ( f sSet <. ( .r ` ndx ) , tpos ( .r ` f ) >. )
13	2, 3, 12	cmpt 4094	. 2 class ( f e. _V |-> ( f sSet <. ( .r ` ndx ) , tpos ( .r ` f ) >. ) )
14	1, 13	wceq 1364	1 wff oppr = ( f e. _V |-> ( f sSet <. ( .r ` ndx ) , tpos ( .r ` f ) >. ) )

This definition is referenced by:  opprvalg  13625