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Mirrors > Home > MPE Home > Th. List > df-gic | Structured version Visualization version Unicode 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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cgic 17700 | . 2 𝑔 | |
2 | cgim 17699 | . . . 4 GrpIso | |
3 | 2 | ccnv 5113 | . . 3 GrpIso |
4 | cvv 3200 | . . . 4 | |
5 | c1o 7553 | . . . 4 | |
6 | 4, 5 | cdif 3571 | . . 3 |
7 | 3, 6 | cima 5117 | . 2 GrpIso |
8 | 1, 7 | wceq 1483 | 1 𝑔 GrpIso |
Colors of variables: wff setvar class |
This definition is referenced by: brgic 17711 gicer 17718 gicerOLD 17719 |
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