Definition df-invr 13295

Description: Define multiplicative inverse. (Contributed by NM, 21-Sep-2011.)

Assertion

Ref	Expression
df-invr	|- invr = ( r e. _V |-> ( invg ` ( (mulGrp ` r ) ↾s (Unit ` r ) ) ) )

Detailed syntax breakdown of Definition df-invr

Step	Hyp	Ref	Expression
1		cinvr 13294	. 2 class invr
2		vr	. . 3 setvar r
3		cvv 2739	. . 3 class _V
4	2	cv 1352	. . . . . 6 class r
5		cmgp 13135	. . . . . 6 class mulGrp
6	4, 5	cfv 5218	. . . . 5 class (mulGrp ` r )
7		cui 13261	. . . . . 6 class Unit
8	4, 7	cfv 5218	. . . . 5 class (Unit ` r )
9		cress 12465	. . . . 5 class ↾s
10	6, 8, 9	co 5877	. . . 4 class ( (mulGrp ` r ) ↾s (Unit ` r ) )
11		cminusg 12883	. . . 4 class invg
12	10, 11	cfv 5218	. . 3 class ( invg ` ( (mulGrp ` r ) ↾s (Unit ` r ) ) )
13	2, 3, 12	cmpt 4066	. 2 class ( r e. _V |-> ( invg ` ( (mulGrp ` r ) ↾s (Unit ` r ) ) ) )
14	1, 13	wceq 1353	1 wff invr = ( r e. _V |-> ( invg ` ( (mulGrp ` r ) ↾s (Unit ` r ) ) ) )

This definition is referenced by:  invrfvald  13296