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Definition df-gic 14740
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 14738 . 2  class  ~=ph𝑔
2 cgim 14737 . . . 4  class GrpIso
32ccnv 4704 . . 3  class  `' GrpIso
4 cvv 2801 . . . 4  class  _V
5 c1o 6488 . . . 4  class  1o
64, 5cdif 3162 . . 3  class  ( _V 
\  1o )
73, 6cima 4708 . 2  class  ( `' GrpIso  " ( _V  \  1o ) )
81, 7wceq 1632 1  wff  ~=ph𝑔  =  ( `' GrpIso  " ( _V  \  1o ) )
Colors of variables: wff set class
This definition is referenced by:  brgic  14749  gicer  14756
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