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Definition df-gic 15876
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  |-  ~=ph𝑔  =  ( `' GrpIso  " ( _V  \  1o ) )

Detailed syntax breakdown of Definition df-gic
StepHypRef Expression
1 cgic 15874 . 2  class  ~=ph𝑔
2 cgim 15873 . . . 4  class GrpIso
32ccnv 4923 . . 3  class  `' GrpIso
4 cvv 3054 . . . 4  class  _V
5 c1o 6999 . . . 4  class  1o
64, 5cdif 3409 . . 3  class  ( _V 
\  1o )
73, 6cima 4927 . 2  class  ( `' GrpIso  " ( _V  \  1o ) )
81, 7wceq 1370 1  wff  ~=ph𝑔  =  ( `' GrpIso  " ( _V  \  1o ) )
Colors of variables: wff setvar class
This definition is referenced by:  brgic  15885  gicer  15892
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