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| Description: Two groups are said to be isomorphic iff they are connected by at least one isomorphism. Isomorphic groups share all global group properties, but to relate local properties requires knowledge of a specific isomorphism. (Contributed by Stefan O'Rear, 25-Jan-2015.) | 
| Ref | Expression | 
|---|---|
| df-gic | ⊢ ≃𝑔 = (◡ GrpIso “ (V ∖ 1o)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | cgic 19276 | . 2 class ≃𝑔 | |
| 2 | cgim 19275 | . . . 4 class GrpIso | |
| 3 | 2 | ccnv 5684 | . . 3 class ◡ GrpIso | 
| 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 (◡ GrpIso “ (V ∖ 1o)) | 
| 8 | 1, 7 | wceq 1540 | 1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o)) | 
| Colors of variables: wff setvar class | 
| This definition is referenced by: brgic 19288 gicer 19295 | 
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