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Mirrors > Home > MPE Home > Th. List > df-gic | Structured version Visualization version GIF version |
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 19049 | . 2 class ≃𝑔 | |
2 | cgim 19048 | . . . 4 class GrpIso | |
3 | 2 | ccnv 5633 | . . 3 class ◡ GrpIso |
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 (◡ GrpIso “ (V ∖ 1o)) |
8 | 1, 7 | wceq 1542 | 1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o)) |
Colors of variables: wff setvar class |
This definition is referenced by: brgic 19060 gicer 19067 |
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