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Definition df-ric 18489
Description: Define the ring isomorphism relation, analogous to df-gic 17473: Two (unital) rings are said to be isomorphic iff they are connected by at least one isomorphism. Isomorphic rings share all global ring properties, but to relate local properties requires knowledge of a specific isomorphism. (Contributed by AV, 24-Dec-2019.)
Assertion
Ref Expression
df-ric 𝑟 = ( RingIso “ (V ∖ 1𝑜))

Detailed syntax breakdown of Definition df-ric
StepHypRef Expression
1 cric 18485 . 2 class 𝑟
2 crs 18484 . . . 4 class RingIso
32ccnv 5026 . . 3 class RingIso
4 cvv 3172 . . . 4 class V
5 c1o 7417 . . . 4 class 1𝑜
64, 5cdif 3536 . . 3 class (V ∖ 1𝑜)
73, 6cima 5030 . 2 class ( RingIso “ (V ∖ 1𝑜))
81, 7wceq 1474 1 wff 𝑟 = ( RingIso “ (V ∖ 1𝑜))
Colors of variables: wff setvar class
This definition is referenced by:  brric  18515
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