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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 18392 | . 2 class ≃𝑔 | |
2 | cgim 18391 | . . . 4 class GrpIso | |
3 | 2 | ccnv 5548 | . . 3 class ◡ GrpIso |
4 | cvv 3494 | . . . 4 class V | |
5 | c1o 8089 | . . . 4 class 1o | |
6 | 4, 5 | cdif 3932 | . . 3 class (V ∖ 1o) |
7 | 3, 6 | cima 5552 | . 2 class (◡ GrpIso “ (V ∖ 1o)) |
8 | 1, 7 | wceq 1533 | 1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o)) |
Colors of variables: wff setvar class |
This definition is referenced by: brgic 18403 gicer 18410 |
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