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Definition df-gic 17473
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.)
Assertion
Ref Expression
df-gic 𝑔 = ( GrpIso “ (V ∖ 1𝑜))

Detailed syntax breakdown of Definition df-gic
StepHypRef Expression
1 cgic 17471 . 2 class 𝑔
2 cgim 17470 . . . 4 class GrpIso
32ccnv 5026 . . 3 class GrpIso
4 cvv 3172 . . . 4 class V
5 c1o 7417 . . . 4 class 1𝑜
64, 5cdif 3536 . . 3 class (V ∖ 1𝑜)
73, 6cima 5030 . 2 class ( GrpIso “ (V ∖ 1𝑜))
81, 7wceq 1474 1 wff 𝑔 = ( GrpIso “ (V ∖ 1𝑜))
Colors of variables: wff setvar class
This definition is referenced by:  brgic  17482  gicer  17489  gicerOLD  17490
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