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Definition df-gic 19100
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 19098 . 2 class 𝑔
2 cgim 19097 . . . 4 class GrpIso
32ccnv 5668 . . 3 class GrpIso
4 cvv 3473 . . . 4 class V
5 c1o 8441 . . . 4 class 1o
64, 5cdif 3941 . . 3 class (V ∖ 1o)
73, 6cima 5672 . 2 class ( GrpIso “ (V ∖ 1o))
81, 7wceq 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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