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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 19278: 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 20471 | . 2 class ≃𝑟 | |
| 2 | crs 20470 | . . . 4 class RingIso | |
| 3 | 2 | ccnv 5684 | . . 3 class ◡ RingIso |
| 4 | cvv 3480 | . . . 4 class V | |
| 5 | c1o 8499 | . . . 4 class 1o | |
| 6 | 4, 5 | cdif 3948 | . . 3 class (V ∖ 1o) |
| 7 | 3, 6 | cima 5688 | . 2 class (◡ RingIso “ (V ∖ 1o)) |
| 8 | 1, 7 | wceq 1540 | 1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o)) |
| Colors of variables: wff setvar class |
| This definition is referenced by: brric 20504 |
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