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Definition df-invr 18444
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
StepHypRef Expression
1 cinvr 18443 . 2 class invr
2 vr . . 3 setvar 𝑟
3 cvv 3173 . . 3 class V
42cv 1474 . . . . . 6 class 𝑟
5 cmgp 18261 . . . . . 6 class mulGrp
64, 5cfv 5790 . . . . 5 class (mulGrp‘𝑟)
7 cui 18411 . . . . . 6 class Unit
84, 7cfv 5790 . . . . 5 class (Unit‘𝑟)
9 cress 15645 . . . . 5 class s
106, 8, 9co 6527 . . . 4 class ((mulGrp‘𝑟) ↾s (Unit‘𝑟))
11 cminusg 17195 . . . 4 class invg
1210, 11cfv 5790 . . 3 class (invg‘((mulGrp‘𝑟) ↾s (Unit‘𝑟)))
132, 3, 12cmpt 4638 . 2 class (𝑟 ∈ V ↦ (invg‘((mulGrp‘𝑟) ↾s (Unit‘𝑟))))
141, 13wceq 1475 1 wff invr = (𝑟 ∈ V ↦ (invg‘((mulGrp‘𝑟) ↾s (Unit‘𝑟))))
Colors of variables: wff setvar class
This definition is referenced by:  invrfval  18445
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