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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 19098 | . 2 class ≃𝑔 | |
2 | cgim 19097 | . . . 4 class GrpIso | |
3 | 2 | ccnv 5668 | . . 3 class ◡ GrpIso |
4 | cvv 3473 | . . . 4 class V | |
5 | c1o 8441 | . . . 4 class 1o | |
6 | 4, 5 | cdif 3941 | . . 3 class (V ∖ 1o) |
7 | 3, 6 | cima 5672 | . 2 class (◡ GrpIso “ (V ∖ 1o)) |
8 | 1, 7 | wceq 1541 | 1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o)) |
Colors of variables: wff setvar class |
This definition is referenced by: brgic 19109 gicer 19116 |
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