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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 18662 | . 2 class ≃𝑔 | |
2 | cgim 18661 | . . . 4 class GrpIso | |
3 | 2 | ccnv 5550 | . . 3 class ◡ GrpIso |
4 | cvv 3408 | . . . 4 class V | |
5 | c1o 8195 | . . . 4 class 1o | |
6 | 4, 5 | cdif 3863 | . . 3 class (V ∖ 1o) |
7 | 3, 6 | cima 5554 | . 2 class (◡ GrpIso “ (V ∖ 1o)) |
8 | 1, 7 | wceq 1543 | 1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o)) |
Colors of variables: wff setvar class |
This definition is referenced by: brgic 18673 gicer 18680 |
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