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Definition df-gic 14724
Description: Two groups are said to be isomorphic iff they are connected by at least one isomorphism. Isomophic 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 14722 . 2  class  ~=ph𝑔
2 cgim 14721 . . . 4  class GrpIso
32ccnv 4688 . . 3  class  `' GrpIso
4 cvv 2788 . . . 4  class  _V
5 c1o 6472 . . . 4  class  1o
64, 5cdif 3149 . . 3  class  ( _V 
\  1o )
73, 6cima 4692 . 2  class  ( `' GrpIso  " ( _V  \  1o ) )
81, 7wceq 1623 1  wff  ~=ph𝑔  =  ( `' GrpIso  " ( _V  \  1o ) )
Colors of variables: wff set class
This definition is referenced by:  brgic  14733  gicer  14740
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