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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 18182 | . 2 class ≃𝑔 | |
2 | cgim 18181 | . . . 4 class GrpIso | |
3 | 2 | ccnv 5403 | . . 3 class ◡ GrpIso |
4 | cvv 3410 | . . . 4 class V | |
5 | c1o 7897 | . . . 4 class 1o | |
6 | 4, 5 | cdif 3821 | . . 3 class (V ∖ 1o) |
7 | 3, 6 | cima 5407 | . 2 class (◡ GrpIso “ (V ∖ 1o)) |
8 | 1, 7 | wceq 1508 | 1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o)) |
Colors of variables: wff setvar class |
This definition is referenced by: brgic 18193 gicer 18200 |
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