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Definition df-ric 20150
Description: Define the ring isomorphism relation, analogous to df-gic 19051: 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 20146 . 2 class 𝑟
2 crs 20145 . . . 4 class RingIso
32ccnv 5633 . . 3 class RingIso
4 cvv 3446 . . . 4 class V
5 c1o 8406 . . . 4 class 1o
64, 5cdif 3908 . . 3 class (V ∖ 1o)
73, 6cima 5637 . 2 class ( RingIso “ (V ∖ 1o))
81, 7wceq 1542 1 wff 𝑟 = ( RingIso “ (V ∖ 1o))
Colors of variables: wff setvar class
This definition is referenced by:  brric  20179
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