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Mirrors > Home > MPE Home > Th. List > df-ric | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
df-ric | ⊢ ≃𝑟 = (◡ RingIso “ (V ∖ 1o)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cric 20146 | . 2 class ≃𝑟 | |
2 | crs 20145 | . . . 4 class RingIso | |
3 | 2 | ccnv 5633 | . . 3 class ◡ RingIso |
4 | cvv 3446 | . . . 4 class V | |
5 | c1o 8406 | . . . 4 class 1o | |
6 | 4, 5 | cdif 3908 | . . 3 class (V ∖ 1o) |
7 | 3, 6 | cima 5637 | . 2 class (◡ RingIso “ (V ∖ 1o)) |
8 | 1, 7 | wceq 1542 | 1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o)) |
Colors of variables: wff setvar class |
This definition is referenced by: brric 20179 |
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