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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 19289 | . 2 class ≃𝑔 | |
2 | cgim 19288 | . . . 4 class GrpIso | |
3 | 2 | ccnv 5688 | . . 3 class ◡ GrpIso |
4 | cvv 3478 | . . . 4 class V | |
5 | c1o 8498 | . . . 4 class 1o | |
6 | 4, 5 | cdif 3960 | . . 3 class (V ∖ 1o) |
7 | 3, 6 | cima 5692 | . 2 class (◡ GrpIso “ (V ∖ 1o)) |
8 | 1, 7 | wceq 1537 | 1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o)) |
Colors of variables: wff setvar class |
This definition is referenced by: brgic 19301 gicer 19308 |
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