Definition df-invr 13617

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

Assertion

Ref	Expression
df-invr	⊢ invr = (𝑟 ∈ V ↦ (invg‘((mulGrp‘𝑟) ↾s (Unit‘𝑟))))

Detailed syntax breakdown of Definition df-invr

Step	Hyp	Ref	Expression
1		cinvr 13616	. 2 class invr
2		vr	. . 3 setvar 𝑟
3		cvv 2760	. . 3 class V
4	2	cv 1363	. . . . . 6 class 𝑟
5		cmgp 13416	. . . . . 6 class mulGrp
6	4, 5	cfv 5254	. . . . 5 class (mulGrp‘𝑟)
7		cui 13583	. . . . . 6 class Unit
8	4, 7	cfv 5254	. . . . 5 class (Unit‘𝑟)
9		cress 12619	. . . . 5 class ↾s
10	6, 8, 9	co 5918	. . . 4 class ((mulGrp‘𝑟) ↾s (Unit‘𝑟))
11		cminusg 13073	. . . 4 class invg
12	10, 11	cfv 5254	. . 3 class (invg‘((mulGrp‘𝑟) ↾s (Unit‘𝑟)))
13	2, 3, 12	cmpt 4090	. 2 class (𝑟 ∈ V ↦ (invg‘((mulGrp‘𝑟) ↾s (Unit‘𝑟))))
14	1, 13	wceq 1364	1 wff invr = (𝑟 ∈ V ↦ (invg‘((mulGrp‘𝑟) ↾s (Unit‘𝑟))))

This definition is referenced by:  invrfvald  13618